title

Richard Karp: Algorithms and Computational Complexity | Lex Fridman Podcast #111

description

Richard Karp is a professor at Berkeley and one of the key figures in the history of theoretical computer science. In 1985, he received the Turing Award for his research in the theory of algorithms, including the development of the Edmonds–Karp algorithm for solving the maximum flow problem on networks, Hopcroft–Karp algorithm for finding maximum cardinality matchings in bipartite graphs, and his landmark paper in complexity theory called "Reducibility Among Combinatorial Problems", in which he proved 21 problems to be NP-complete. This paper was probably the most important catalyst in the explosion of interest in the study of NP-completeness and the P vs NP problem.
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EPISODE LINKS:
Richard's wikipedia: https://en.wikipedia.org/wiki/Richard_M._Karp
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Full episodes playlist:
https://www.youtube.com/playlist?list=PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4
Clips playlist:
https://www.youtube.com/playlist?list=PLrAXtmErZgOeciFP3CBCIEElOJeitOr41
OUTLINE:
0:00 - Introduction
3:50 - Geometry
9:46 - Visualizing an algorithm
13:00 - A beautiful algorithm
18:06 - Don Knuth and geeks
22:06 - Early days of computers
25:53 - Turing Test
30:05 - Consciousness
33:22 - Combinatorial algorithms
37:42 - Edmonds-Karp algorithm
40:22 - Algorithmic complexity
50:25 - P=NP
54:25 - NP-Complete problems
1:10:29 - Proving P=NP
1:12:57 - Stable marriage problem
1:20:32 - Randomized algorithms
1:33:23 - Can a hard problem be easy in practice?
1:43:57 - Open problems in theoretical computer science
1:46:21 - A strange idea in complexity theory
1:50:49 - Machine learning
1:56:26 - Bioinformatics
2:00:37 - Memory of Richard's father
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detail

{'title': 'Richard Karp: Algorithms and Computational Complexity | Lex Fridman Podcast #111', 'heatmap': [{'end': 5375.027, 'start': 5272.532, 'weight': 1}], 'summary': 'Richard karp, a turing award winner, is discussed for his work in algorithms and complexity theory, including proving 21 problems to be np-complete. various topics such as ai limitations, network flow optimization, p vs. np problem, stable matching algorithm, and randomized algorithms are also covered in the podcast.', 'chapters': [{'end': 48.351, 'segs': [{'end': 48.351, 'src': 'embed', 'start': 21.879, 'weight': 0, 'content': [{'end': 35.344, 'text': 'Hopcroft-Karp algorithm for finding maximum cardinality matchings in bipartite graphs and his landmark paper in complexity theory called Reducibility Among Combinatorial Problems,', 'start': 21.879, 'duration': 13.465}, {'end': 38.445, 'text': 'in which he proved 21 problems to be NP-complete.', 'start': 35.344, 'duration': 3.101}, {'end': 48.351, 'text': 'This paper was probably the most important catalyst in the explosion of interest in the study of NP completeness and the P versus NP problem in general.', 'start': 39.065, 'duration': 9.286}], 'summary': 'Hopcroft-karp algorithm finds max cardinality matchings and proves 21 problems np-complete, sparking interest in p versus np problem.', 'duration': 26.472, 'max_score': 21.879, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs21879.jpg'}], 'start': 0.089, 'title': "Richard karp's work", 'summary': "Discusses richard karp, a leading figure in theoretical computer science who won the turing award in 1985. karp's influential research in algorithms and complexity theory, including proving 21 problems to be np-complete, sparked widespread interest in the study of np completeness and the p versus np problem.", 'chapters': [{'end': 48.351, 'start': 0.089, 'title': 'Richard karp: leading theoretical computer scientist', 'summary': 'Discusses richard karp, a prominent figure in theoretical computer science, who won the turing award in 1985 for his influential research in algorithms and complexity theory, such as proving 21 problems to be np-complete, which sparked widespread interest in the study of np completeness and the p versus np problem.', 'duration': 48.262, 'highlights': ['Richard Karp received the Turing Award in 1985 for his research in the theory of algorithms, including the development of influential algorithms like the Admiralty-Karp algorithm and the Hopcroft-Karp algorithm.', "Karp's landmark paper in complexity theory, 'Reducibility Among Combinatorial Problems,' proved 21 problems to be NP-complete, which had a significant impact on the study of NP completeness and the P versus NP problem.", 'The paper was a catalyst in the explosion of interest in the study of NP completeness and the P versus NP problem in general.']}], 'duration': 48.262, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs89.jpg', 'highlights': ["Karp's landmark paper proved 21 problems to be NP-complete, impacting the study of NP completeness and the P versus NP problem.", 'Richard Karp received the Turing Award in 1985 for his influential research in algorithms and complexity theory.', "The Admiralty-Karp algorithm and the Hopcroft-Karp algorithm are among Karp's influential algorithm developments."]}, {'end': 1297.788, 'segs': [{'end': 92.414, 'src': 'embed', 'start': 48.831, 'weight': 0, 'content': [{'end': 49.872, 'text': 'Quick summary of the ads.', 'start': 48.831, 'duration': 1.041}, {'end': 53.114, 'text': 'Two sponsors, 8 Sleep Mattress and Cash App.', 'start': 50.252, 'duration': 2.862}, {'end': 62.54, 'text': 'Please consider supporting this podcast by going to 8sleep.com slash Lex and downloading Cash App and using code LexPodcast.', 'start': 53.594, 'duration': 8.946}, {'end': 64.381, 'text': 'Click the links, buy the stuff.', 'start': 63.08, 'duration': 1.301}, {'end': 67.123, 'text': 'It really is the best way to support this podcast.', 'start': 64.721, 'duration': 2.402}, {'end': 72.523, 'text': 'If you enjoy this thing, subscribe on YouTube, review it with five stars on Apple Podcasts,', 'start': 68.12, 'duration': 4.403}, {'end': 75.965, 'text': 'support it on Patreon or connect with me on Twitter at Lex Friedman.', 'start': 72.523, 'duration': 3.442}, {'end': 82.048, 'text': "As usual, I'll do a few minutes of ads now and never any ads in the middle that can break the flow of the conversation.", 'start': 76.865, 'duration': 5.183}, {'end': 92.414, 'text': 'This show is sponsored by Eight Sleep and its Pod Pro mattress that you can check out at eightsleep.com slash Lex to get $200 off.', 'start': 83.029, 'duration': 9.385}], 'summary': 'Podcast features two sponsors, 8 sleep mattress and cash app, promoting support through purchases and engagement.', 'duration': 43.583, 'max_score': 48.831, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs48831.jpg'}, {'end': 141.254, 'src': 'embed', 'start': 110.23, 'weight': 12, 'content': [{'end': 117.755, 'text': "I've just been really enjoying it, both in the fact that I'm getting better sleep and that it's a smart mattress, essentially.", 'start': 110.23, 'duration': 7.525}, {'end': 124.202, 'text': 'I kind of imagine this being the early days of artificial intelligence being a part of every aspect of our lives.', 'start': 117.775, 'duration': 6.427}, {'end': 132.274, 'text': 'And certainly infusing AI in one of the most important aspects of life, which is sleep, I think has a lot of potential for being beneficial.', 'start': 124.443, 'duration': 7.831}, {'end': 141.254, 'text': 'The Pod Pro is packed with sensors that track heart rate, heart rate variability, and respiratory rate, showing it all in their app.', 'start': 133.168, 'duration': 8.086}], 'summary': 'The pod pro smart mattress improves sleep with ai and sensors, tracking heart rate and respiratory rate.', 'duration': 31.024, 'max_score': 110.23, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs110230.jpg'}, {'end': 184.702, 'src': 'embed', 'start': 158.088, 'weight': 5, 'content': [{'end': 166.172, 'text': 'just visiting the site and considering the purchase helps convince the folks at ASleep that this silly old podcast is worth sponsoring in the future.', 'start': 158.088, 'duration': 8.084}, {'end': 175.017, 'text': 'This show is also presented by the great and powerful Cash App, the number one finance app in the App Store.', 'start': 167.493, 'duration': 7.524}, {'end': 177.718, 'text': 'When you get it, use code LEXPODCAST.', 'start': 175.377, 'duration': 2.341}, {'end': 184.702, 'text': 'Cash App lets you send money to friends, buy Bitcoin, and invest in the stock market with as little as $1.', 'start': 178.219, 'duration': 6.483}], 'summary': 'Visiting the site can convince asleep to sponsor, and cash app allows investing with $1.', 'duration': 26.614, 'max_score': 158.088, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs158088.jpg'}, {'end': 229.294, 'src': 'embed', 'start': 199.316, 'weight': 4, 'content': [{'end': 202.419, 'text': "I'm looking at you, Clippy, from Microsoft, even though I love you.", 'start': 199.316, 'duration': 3.103}, {'end': 209.544, 'text': "Anyway, there's a big part of my brain and heart that loves to design things and also to appreciate great design by others.", 'start': 203.2, 'duration': 6.344}, {'end': 216.067, 'text': 'So again, if you get Cash App from the App Store or Google Play and use the code LexPodcast, you get $10.', 'start': 210.064, 'duration': 6.003}, {'end': 224.752, 'text': 'And Cash App will also donate $10 to FIRST, an organization that is helping to advance robotics and STEM education for young people around the world.', 'start': 216.067, 'duration': 8.685}, {'end': 229.294, 'text': "And now, here's my conversation with Richard Karp.", 'start': 225.772, 'duration': 3.522}], 'summary': 'Promotion for cash app: $10 for users, $10 donation to first', 'duration': 29.978, 'max_score': 199.316, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs199316.jpg'}, {'end': 894.723, 'src': 'embed', 'start': 815.468, 'weight': 2, 'content': [{'end': 832.662, 'text': 'you have n boys and n girls and you are given the desirability or the cost of matching the ith boy with the jth girl for all i and j.', 'start': 815.468, 'duration': 17.194}, {'end': 844.354, 'text': "You're given a matrix of numbers And you want to find the one-to-one matching of the boys with the girls,", 'start': 832.662, 'duration': 11.692}, {'end': 848.516, 'text': 'such that the sum of the associated costs will be minimized.', 'start': 844.354, 'duration': 4.162}, {'end': 856.158, 'text': 'So the best way to match the boys with the girls or men with jobs or any two sets.', 'start': 848.776, 'duration': 7.382}, {'end': 866.044, 'text': 'Any possible matching is possible? Yeah, all one-to-one correspondences are permissible.', 'start': 858.539, 'duration': 7.505}, {'end': 874.71, 'text': 'If there is a connection that is not allowed, then you can think of it as having an infinite cost.', 'start': 866.885, 'duration': 7.825}, {'end': 894.723, 'text': 'So what you do is to depend on the observation that the identity of the optimal assignment, or as we call it, the optimal permutation,', 'start': 874.73, 'duration': 19.993}], 'summary': 'Given n boys and n girls, find the one-to-one matching with minimum cost.', 'duration': 79.255, 'max_score': 815.468, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs815468.jpg'}, {'end': 960.571, 'src': 'embed', 'start': 925.28, 'weight': 1, 'content': [{'end': 948.504, 'text': 'So the idea of the algorithm is to start with a matrix of non-negative numbers and keep subtracting from rows or entire columns in such a way that you subtract the same constant from all the elements of that row or column,', 'start': 925.28, 'duration': 23.224}, {'end': 956.329, 'text': 'while maintaining the property that all the elements are non-negative.', 'start': 948.504, 'duration': 7.825}, {'end': 960.571, 'text': 'Simple Yeah.', 'start': 958.49, 'duration': 2.081}], 'summary': 'Algorithm starts with a matrix, subtracts same constant from rows/columns, ensuring non-negative elements.', 'duration': 35.291, 'max_score': 925.28, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs925280.jpg'}], 'start': 48.831, 'title': 'Various topics in geometry and algorithms', 'summary': "Discusses the benefits of eight sleep pod pro mattress and cash app's financial functionalities, the elegance and power of formal proofs in plane geometry, the impact of geometry on combinatorial algorithms, and the algorithm for optimal matching of sets.", 'chapters': [{'end': 216.067, 'start': 48.831, 'title': 'Smart mattress and finance app ads', 'summary': "Discusses the benefits of the eight sleep pod pro mattress, including its temperature control feature, and the cash app's design and financial functionalities, while promoting their support for the podcast.", 'duration': 167.236, 'highlights': ['The Eight Sleep Pod Pro mattress offers a $200 discount when purchased through eightsleep.com/Lex, with temperature control down to 55 degrees on each side of the bed. The mattress provides a significant discount and highlights its unique temperature control feature, which can impact sleep quality.', "The mattress is equipped with sensors that track heart rate, heart rate variability, and respiratory rate, displaying the data in their app. The mattress's app showcases health metrics, adding to its appeal and potential benefits for users.", "Cash App, the podcast's other sponsor, offers $10 when using the code LexPodcast, enabling users to send money, buy Bitcoin, and invest with as little as $1. The Cash App's financial functionalities and user-friendly design are highlighted, emphasizing its appeal to potential users."]}, {'end': 513.597, 'start': 216.067, 'title': 'Elegance of geometry and proofs', 'summary': "Discusses the elegance and power of formal proofs in plane geometry, highlighting michael rabin's elegant solution for finding the shortest distance between two non-overlapping circles and richard karp's enjoyment of establishing geometric facts through pure reasoning.", 'duration': 297.53, 'highlights': ["Michael Rabin's elegant solution for finding the shortest distance between two non-overlapping circles based on pure reasoning. Michael Rabin provided an elegant solution for finding the shortest distance between two non-overlapping circles by using pure reasoning, stating that the straight line between the two centers is the shortest distance and any other line connecting the circles would be longer.", "Richard Karp's enjoyment of establishing geometric facts through pure reasoning and finding puzzles in plane geometry more fun than arithmetic operations. Richard Karp found joy in establishing geometric facts through pure reasoning and solving puzzles in plane geometry, finding it more enjoyable than arithmetic operations.", 'The surprise and convincing nature of proving that the sum of the angles of a triangle is 180 degrees. The proof that the sum of the angles of a triangle is 180 degrees was described as surprising and convincing, as it involved drawing a line parallel to the opposite side, which trisects the angle and creates a half plane that adds up to 180 degrees.']}, {'end': 815.468, 'start': 514.787, 'title': 'Impact of geometry on combinatorial algorithms', 'summary': 'Discusses the impact of geometry on combinatorial algorithms, particularly focusing on the use of tools like linear programming and integer programming, the visualization of algorithms, and the mechanics of solving problems such as the traveling salesman problem.', 'duration': 300.681, 'highlights': ['The use of tools like linear programming and integer programming require high-dimensional visualization and leaning on algebraic properties. The speaker emphasizes the reliance on algebraic properties and the challenge of high-dimensional visualization when using tools like linear programming and integer programming.', 'Visualizing the mechanics of algorithms involves iteratively reducing the distance from the desired solution and continually making progress towards the optimum point. The speaker describes the visualization of algorithm mechanics as iteratively reducing the distance from the desired solution and making progress towards the optimum point.', 'The fascination with observing successive approaches to the optimum in solving problems like the traveling salesman problem. The speaker expresses fascination in observing successive approaches to the optimum while solving problems like the traveling salesman problem, demonstrating the engaging nature of algorithmic problem-solving.', 'The magic lies in the fact that the gap from the optimum decreases monotonically, with various metrics improving until the optimum is reached. The speaker highlights the magic of algorithmic problem-solving, where the gap from the optimum decreases monotonically and various metrics improve until reaching the optimum.', 'Discussion of the assignment problem and the Hungarian algorithm, illustrating the aesthetic pleasure derived from contemplating the structure of computational processes. The chapter delves into the assignment problem and the Hungarian algorithm, showcasing the aesthetic pleasure derived from contemplating the structure of computational processes.']}, {'end': 1297.788, 'start': 815.468, 'title': 'Optimal matching of sets', 'summary': 'Discusses the algorithm for finding the one-to-one matching of boys with girls or men with jobs, minimizing the sum of associated costs by subtracting constants from rows or columns in a matrix and finding the shortest path through the elements.', 'duration': 482.32, 'highlights': ['The algorithm aims to find the one-to-one matching of sets by subtracting constants from rows or columns in a matrix while maintaining the property that all elements are non-negative. The algorithm focuses on minimizing the sum of associated costs by subtracting constants from rows or columns in a matrix while maintaining non-negativity, leading to the optimal matching of sets.', 'The iterative algorithm keeps subtracting from rows or entire columns in a way that decreases the total cost while maintaining non-negative elements, ultimately resulting in a full permutation of zeros, which signifies the cheapest option. The iterative algorithm systematically subtracts constants from rows or columns, maintaining non-negativity, and aims to achieve a full permutation of zeros, indicating the most cost-effective solution.', 'The systematic and elegant nature of the iterative algorithm is highlighted, evoking a sense of beauty and satisfaction, akin to shaping something into a beautiful and orderly form. The systematic and elegant nature of the iterative algorithm is found to be aesthetically pleasing, resonating with the satisfaction derived from shaping something into a beautiful and orderly form.']}], 'duration': 1248.957, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs48831.jpg', 'highlights': ['The Eight Sleep Pod Pro mattress offers a $200 discount with temperature control down to 55 degrees on each side of the bed.', 'The mattress is equipped with sensors that track heart rate, heart rate variability, and respiratory rate, displaying the data in their app.', 'Cash App offers $10 when using the code LexPodcast, enabling users to send money, buy Bitcoin, and invest with as little as $1.', 'Michael Rabin provided an elegant solution for finding the shortest distance between two non-overlapping circles by using pure reasoning.', 'Richard Karp found joy in establishing geometric facts through pure reasoning and solving puzzles in plane geometry.', 'The proof that the sum of the angles of a triangle is 180 degrees was described as surprising and convincing.', 'The use of tools like linear programming and integer programming require high-dimensional visualization and leaning on algebraic properties.', 'Visualizing the mechanics of algorithms involves iteratively reducing the distance from the desired solution and continually making progress towards the optimum point.', 'The fascination with observing successive approaches to the optimum in solving problems like the traveling salesman problem.', 'The magic of algorithmic problem-solving, where the gap from the optimum decreases monotonically and various metrics improve until reaching the optimum.', 'The chapter delves into the assignment problem and the Hungarian algorithm, showcasing the aesthetic pleasure derived from contemplating the structure of computational processes.', 'The algorithm focuses on minimizing the sum of associated costs by subtracting constants from rows or columns in a matrix while maintaining non-negativity, leading to the optimal matching of sets.', 'The iterative algorithm systematically subtracts constants from rows or columns, maintaining non-negativity, and aims to achieve a full permutation of zeros, indicating the most cost-effective solution.', 'The systematic and elegant nature of the iterative algorithm is found to be aesthetically pleasing, resonating with the satisfaction derived from shaping something into a beautiful and orderly form.']}, {'end': 1984.038, 'segs': [{'end': 1831.026, 'src': 'embed', 'start': 1769.439, 'weight': 0, 'content': [{'end': 1784.332, 'text': 'So there is, however, an existence proof that, if you believe that the brain is, is just a network of neurons operating by rules.', 'start': 1769.439, 'duration': 14.893}, {'end': 1790.959, 'text': "I guess you could say that that's an existence proof of the capabilities of a mechanism.", 'start': 1784.332, 'duration': 6.627}, {'end': 1802.11, 'text': 'But it would be almost impossible to acquire the information unless we got enough insight into the operation of the brain.', 'start': 1792.36, 'duration': 9.75}, {'end': 1804.117, 'text': "But there's so much mystery there.", 'start': 1802.756, 'duration': 1.361}, {'end': 1807.279, 'text': 'What do you make of consciousness, for example?', 'start': 1804.497, 'duration': 2.782}, {'end': 1815.164, 'text': 'As an example of something we completely have no clue about the fact that we have this subjective experience.', 'start': 1809.961, 'duration': 5.203}, {'end': 1826.171, 'text': 'Is it possible that this network of this circuit of switches is able to create something like consciousness? To know its own identity.', 'start': 1816.004, 'duration': 10.167}, {'end': 1829.705, 'text': 'Yeah, to know the algorithm, to know itself.', 'start': 1826.843, 'duration': 2.862}, {'end': 1831.026, 'text': 'To know itself.', 'start': 1830.285, 'duration': 0.741}], 'summary': "The brain's mystery and consciousness challenge our understanding of its capabilities and operation.", 'duration': 61.587, 'max_score': 1769.439, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs1769439.jpg'}, {'end': 1984.038, 'src': 'embed', 'start': 1954.6, 'weight': 1, 'content': [{'end': 1965.065, 'text': 'Or, on the flip side, is it possible that also intelligence is actually way, way, way, way harder, even with exponential improvement,', 'start': 1954.6, 'duration': 10.465}, {'end': 1966.006, 'text': 'to be able to crack?', 'start': 1965.065, 'duration': 0.941}, {'end': 1974.139, 'text': "I don't think any constant factor improvement could change things.", 'start': 1967.136, 'duration': 7.003}, {'end': 1984.038, 'text': 'Given our current comprehension of how of what cognition requires.', 'start': 1974.26, 'duration': 9.778}], 'summary': 'Cracking intelligence may be exponentially harder despite improvements.', 'duration': 29.438, 'max_score': 1954.6, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs1954600.jpg'}], 'start': 1299.148, 'title': 'Artificial intelligence', 'summary': 'Discusses the early history of computers and skepticism towards achieving human-level intelligence, highlighting the limitations of current ai. it also delves into the doubts about achieving general intelligence and consciousness in artificial intelligence and the challenges in replicating human cognition.', 'chapters': [{'end': 1768.439, 'start': 1299.148, 'title': 'Early computers and artificial intelligence', 'summary': 'Discusses the early history of computers and the skepticism towards achieving human-level intelligence through algorithms, highlighting the limitations of current achievements in ai in comparison to human cognitive abilities and emotions.', 'duration': 469.291, 'highlights': ['The chapter delves into the early history of computers, depicting the size and complexity of machines like the Mark IV and UNIVAC, providing a glimpse into the evolution of computing technology.', 'The discussion explores the skepticism towards achieving human-level intelligence through algorithms, emphasizing the limitations of current AI achievements in replicating human cognitive abilities and emotions.', 'The conversation addresses the skepticism regarding the possibility of reducing the complexity of human intelligence to a set of algorithms, raising doubts about whether a Turing machine can achieve human-level intelligence.', 'The interviewee expresses skepticism about the feasibility of replicating human intelligence through algorithms, asserting that the current achievements in AI do not come close to encompassing the full range of human cognitive abilities and emotions.']}, {'end': 1984.038, 'start': 1769.439, 'title': 'The future of artificial intelligence', 'summary': 'Discusses the limitations of achieving general intelligence and consciousness in artificial intelligence, expressing doubt about the singularity and exponential improvement, and highlighting the challenges in replicating human cognition.', 'duration': 214.599, 'highlights': ['The challenge of replicating consciousness and general intelligence in artificial intelligence is highlighted, expressing doubt about the singularity and the possibility of machines surpassing humans (Relevance: 5)', 'The limitations of achieving general intelligence and consciousness in artificial intelligence are discussed, emphasizing the difficulty in replicating human cognition (Relevance: 4)', 'The skepticism towards exponential improvement in artificial intelligence and the challenge in comprehending the potential for significant leaps in intelligence are expressed (Relevance: 3)', 'The concern over the existential threat of artificial intelligence surpassing human capabilities is mentioned, questioning the possibility of machines reaching a level of cognition comparable to humans (Relevance: 2)']}], 'duration': 684.89, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs1299148.jpg', 'highlights': ['The chapter delves into the early history of computers, depicting the size and complexity of machines like the Mark IV and UNIVAC, providing a glimpse into the evolution of computing technology.', 'The discussion explores the skepticism towards achieving human-level intelligence through algorithms, emphasizing the limitations of current AI achievements in replicating human cognitive abilities and emotions.', 'The conversation addresses the skepticism regarding the possibility of reducing the complexity of human intelligence to a set of algorithms, raising doubts about whether a Turing machine can achieve human-level intelligence.', 'The interviewee expresses skepticism about the feasibility of replicating human intelligence through algorithms, asserting that the current achievements in AI do not come close to encompassing the full range of human cognitive abilities and emotions.', 'The challenge of replicating consciousness and general intelligence in artificial intelligence is highlighted, expressing doubt about the singularity and the possibility of machines surpassing humans (Relevance: 5)', 'The limitations of achieving general intelligence and consciousness in artificial intelligence are discussed, emphasizing the difficulty in replicating human cognition (Relevance: 4)', 'The skepticism towards exponential improvement in artificial intelligence and the challenge in comprehending the potential for significant leaps in intelligence are expressed (Relevance: 3)', 'The concern over the existential threat of artificial intelligence surpassing human capabilities is mentioned, questioning the possibility of machines reaching a level of cognition comparable to humans (Relevance: 2)']}, {'end': 2704.173, 'segs': [{'end': 2216.86, 'src': 'embed', 'start': 2182.902, 'weight': 5, 'content': [{'end': 2197.009, 'text': 'are the individual classes and the edges indicate the constraints which say that certain classes cannot take place at the same time or certain teachers are available only for certain classes,', 'start': 2182.902, 'duration': 14.107}, {'end': 2197.149, 'text': 'etc.', 'start': 2197.009, 'duration': 0.14}, {'end': 2207.992, 'text': 'Or I talked earlier about the assignment problem of matching the boys with the girls,', 'start': 2198.662, 'duration': 9.33}, {'end': 2216.86, 'text': 'where you have there a graph with an edge from each boy to each girl with a weight indicating the cost.', 'start': 2207.992, 'duration': 8.868}], 'summary': 'Transcript discusses constraints in class scheduling and the assignment problem of matching boys with girls using a weighted graph.', 'duration': 33.958, 'max_score': 2182.902, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs2182902.jpg'}, {'end': 2437.675, 'src': 'embed', 'start': 2408.448, 'weight': 2, 'content': [{'end': 2415.091, 'text': 'So what was it like tackling that problem and trying to arrive at a polynomial time solution?', 'start': 2408.448, 'duration': 6.643}, {'end': 2417.192, 'text': 'And maybe you can describe the algorithm.', 'start': 2415.691, 'duration': 1.501}, {'end': 2420.453, 'text': "maybe you can describe what's the running time complexity that you showed.", 'start': 2417.192, 'duration': 3.261}, {'end': 2429.913, 'text': 'Yeah Well, first of all, what is a polynomial time algorithm? Perhaps we could Discuss that.', 'start': 2420.693, 'duration': 9.22}, {'end': 2434.114, 'text': 'Yeah, What is algorithmic complexity?', 'start': 2430.173, 'duration': 3.941}, {'end': 2437.675, 'text': 'What are the major classes of algorithm complexity?', 'start': 2434.174, 'duration': 3.501}], 'summary': 'Discussion on polynomial time solutions and algorithmic complexity', 'duration': 29.227, 'max_score': 2408.448, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs2408448.jpg'}, {'end': 2558.915, 'src': 'embed', 'start': 2529.134, 'weight': 0, 'content': [{'end': 2534.837, 'text': 'the number of basic computational steps grows only as some fixed power of that size.', 'start': 2529.134, 'duration': 5.703}, {'end': 2544.122, 'text': 'A linear algorithm would execute a number of steps linearly proportional to the size.', 'start': 2534.857, 'duration': 9.265}, {'end': 2549.427, 'text': 'Quadratic algorithm would be steps proportional to the square of the size and so on.', 'start': 2544.703, 'duration': 4.724}, {'end': 2558.915, 'text': 'And algorithms whose running time is bounded by some fixed power of the size are called polynomial algorithms.', 'start': 2550.788, 'duration': 8.127}], 'summary': 'Algorithms with running time bounded by fixed power of size are polynomial.', 'duration': 29.781, 'max_score': 2529.134, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs2529134.jpg'}], 'start': 1984.899, 'title': 'Combinatorial algorithms and network flows', 'summary': 'Covers combinatorial algorithms applied in optimizing network efficiency with examples such as school scheduling and computer design. it also discusses the development of a polynomial time algorithm for solving the maximum flow problem, emphasizing algorithmic complexity and efficiency in large networks.', 'chapters': [{'end': 2262.045, 'start': 1984.899, 'title': 'Combinatorial algorithms in networks', 'summary': 'Introduces combinatorial algorithms and their applications in optimizing network efficiency, including examples such as scheduling classes at a school and logical design of computers. it also defines a graph and its significance in representing interconnections between discrete objects.', 'duration': 277.146, 'highlights': ['A graph represents the interconnections between discrete objects in various applications, such as switches in a digital circuit or communication patterns in a human community. Graphs serve to represent interconnections, whether in digital circuits or human communities, and can be directed or undirected.', 'Combinatorial algorithms aim to optimize the efficiency of networks and solve problems like scheduling classes at a school and logical design of computers. The algorithms are applied to optimize network efficiency and solve problems like scheduling classes and logical design of computers.', 'Combinatorial algorithms deal with discrete objects and aim to minimize some cost function or prove the existence of a combinatorial configuration, as seen in examples like coloring the vertices of a graph. The algorithms handle discrete objects and work to minimize costs or prove combinatorial configurations, exemplified by vertex coloring in graphs.']}, {'end': 2704.173, 'start': 2263.044, 'title': 'Network flows and polynomial time algorithms', 'summary': 'Discusses the compelling nature of network flows and the development of a polynomial time algorithm to solve the maximum flow problem, providing insights into algorithmic complexity and classes of algorithm complexity, with a focus on polynomial time algorithms and their efficiency in large networks.', 'duration': 441.129, 'highlights': ['The chapter discusses the development of a polynomial time algorithm to solve the maximum flow problem, providing insights into algorithmic complexity and classes of algorithm complexity, with a focus on polynomial time algorithms and their efficiency in large networks. Development of a polynomial time algorithm for maximum flow problem, insights into algorithmic complexity and classes of algorithm complexity, focus on efficiency in large networks', 'The chapter explores the visually and intellectually compelling nature of network flows and their applications in communication networks, traffic flow, and supply chains. Visually and intellectually compelling nature of network flows, applications in communication networks, traffic flow, and supply chains', 'The chapter highlights the fundamental combinatorial problem of determining the maximum rate at which information can flow along communication channels in a network, with a formal proof for solving the maximum flow problem in polynomial time. Fundamental combinatorial problem of determining maximum flow rate, formal proof for solving maximum flow problem in polynomial time']}], 'duration': 719.274, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs1984899.jpg', 'highlights': ['Development of a polynomial time algorithm for maximum flow problem, insights into algorithmic complexity and classes of algorithm complexity, focus on efficiency in large networks', 'Fundamental combinatorial problem of determining maximum flow rate, formal proof for solving maximum flow problem in polynomial time', 'Visually and intellectually compelling nature of network flows, applications in communication networks, traffic flow, and supply chains', 'Combinatorial algorithms deal with discrete objects and aim to minimize some cost function or prove the existence of a combinatorial configuration, as seen in examples like coloring the vertices of a graph', 'Combinatorial algorithms aim to optimize the efficiency of networks and solve problems like scheduling classes at a school and logical design of computers. The algorithms are applied to optimize network efficiency and solve problems like scheduling classes and logical design of computers', 'A graph represents the interconnections between discrete objects in various applications, such as switches in a digital circuit or communication patterns in a human community. Graphs serve to represent interconnections, whether in digital circuits or human communities, and can be directed or undirected']}, {'end': 3185.899, 'segs': [{'end': 2746.145, 'src': 'embed', 'start': 2705.874, 'weight': 0, 'content': [{'end': 2710.576, 'text': "That's a very important issue because, as we may discuss later,", 'start': 2705.874, 'duration': 4.702}, {'end': 2719.521, 'text': "there are some very important algorithms which don't have a good standing from the point of view of their worst-case performance and yet are very effective.", 'start': 2710.576, 'duration': 8.945}, {'end': 2727.245, 'text': 'Theoreticians are interested in P, the class of problems solvable in polynomial time.', 'start': 2722.323, 'duration': 4.922}, {'end': 2746.145, 'text': "Then there's NP, which is the class of problems which may be hard to solve, but when confronted with a solution, you can check it in polynomial time.", 'start': 2729.186, 'duration': 16.959}], 'summary': 'Theoretical interest in p and np classes for problem-solving algorithms.', 'duration': 40.271, 'max_score': 2705.874, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs2705874.jpg'}, {'end': 2801.43, 'src': 'embed', 'start': 2764.038, 'weight': 3, 'content': [{'end': 2770.746, 'text': 'And the question is, how many steps are needed to solve it.', 'start': 2764.038, 'duration': 6.708}, {'end': 2783.092, 'text': 'And Jack Edmonds and I were the first to show that it could be done in time n cubed, earlier algorithms required into the fourth.', 'start': 2771.786, 'duration': 11.306}, {'end': 2788.935, 'text': 'So as a polynomial function of the size of the input, this is a fast algorithm.', 'start': 2783.973, 'duration': 4.962}, {'end': 2801.43, 'text': 'Now to illustrate the class NP, the question is how long would it take to verify that a solution is optimal.', 'start': 2790.196, 'duration': 11.234}], 'summary': 'Algorithm can solve in n cubed steps, faster than previous n^4.', 'duration': 37.392, 'max_score': 2764.038, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs2764038.jpg'}, {'end': 3032.671, 'src': 'embed', 'start': 3006.16, 'weight': 5, 'content': [{'end': 3014.046, 'text': 'checking is easier and therefore the class of problems that can be checked appears to be much larger than the class of problems that can be solved.', 'start': 3006.16, 'duration': 7.886}, {'end': 3023.764, 'text': "And then you keep adding appears to and sort of these additional words that designate that we don't know for sure yet.", 'start': 3014.616, 'duration': 9.148}, {'end': 3025.145, 'text': "We don't know for sure.", 'start': 3024.044, 'duration': 1.101}, {'end': 3032.671, 'text': 'So the theoretical question, which is considered to be the most central problem in theoretical computer science,', 'start': 3025.225, 'duration': 7.446}], 'summary': 'Checking is easier than solving, raising theoretical questions in computer science.', 'duration': 26.511, 'max_score': 3006.16, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs3006160.jpg'}], 'start': 2705.874, 'title': 'P vs. np problem', 'summary': 'Delves into the significance of algorithms with poor worst-case performance but high effectiveness, introduces classes p and np, and presents an example of the assignment problem with a time complexity of n cubed. it also explores cliques in graphs, the challenges of solving np problems, and skepticism about p equaling np, with a specific reference to factoring large numbers.', 'chapters': [{'end': 2801.43, 'start': 2705.874, 'title': 'P vs. np: algorithms and complexity', 'summary': 'Discusses the importance of algorithms with poor worst-case performance but high effectiveness, and introduces the classes p and np, showcasing an example of the assignment problem with an algorithm of time complexity n cubed.', 'duration': 95.556, 'highlights': ['The class NP is introduced, which consists of problems that may be hard to solve, but when given a solution, it can be verified in polynomial time, such as the assignment problem with a time complexity of n cubed.', 'The importance of algorithms with poor worst-case performance yet high effectiveness is highlighted, indicating the focus of theoreticians on the class P, which includes problems solvable in polynomial time.', 'The example of the assignment problem is presented, demonstrating the reduction in time complexity from n^4 to n^3 with Jack Edmonds, emphasizing the efficiency of the algorithm in polynomial time.']}, {'end': 3185.899, 'start': 2802.711, 'title': 'P vs np: a fundamental problem', 'summary': 'Discusses the concept of cliques in graphs, the distinction between finding and verifying cliques, and the p vs np problem, highlighting the difficulty in solving np problems and the skepticism regarding p equaling np, with a specific reference to the problem of factoring large numbers.', 'duration': 383.188, 'highlights': ["The distinction between finding and verifying cliques in graphs is emphasized, with the former being a hard problem and the latter being easy to verify. It's highlighted that finding the clique in a graph is a hard problem, while checking it is easy, illustrating the concept of non-deterministic polynomial time algorithms (NP) and the class NP.", 'The concept of NP problems being easy to verify but hard to solve is discussed, with the comparison between the class NP and class P, indicating the potential difficulty in solving NP problems. The discussion outlines the distinction between problems in the class NP, which are easy to check but potentially hard to solve, and the class P, suggesting that NP problems may pose greater solving challenges.', 'The skepticism regarding P equaling NP is highlighted, with a bet placed on P being unequal to NP due to the historical lack of efficient solutions for longstanding mathematical problems. The skepticism around P equaling NP is emphasized, with a bet placed on P being unequal to NP due to the historical absence of efficient solutions for long-standing mathematical problems, such as factoring large numbers.']}], 'duration': 480.025, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs2705874.jpg', 'highlights': ['The class NP is introduced, consisting of problems hard to solve but verifiable in polynomial time, e.g., assignment problem with n cubed time complexity.', 'Importance of algorithms with poor worst-case performance yet high effectiveness is highlighted, focusing on problems solvable in polynomial time.', 'Example of the assignment problem is presented, demonstrating reduction in time complexity from n^4 to n^3 with Jack Edmonds, emphasizing efficiency of algorithm in polynomial time.', 'Distinction between finding and verifying cliques in graphs is emphasized, illustrating the concept of non-deterministic polynomial time algorithms (NP) and the class NP.', 'Concept of NP problems being easy to verify but hard to solve is discussed, outlining the distinction between problems in class NP and class P.', 'Skepticism regarding P equaling NP is highlighted, with a bet placed on P being unequal to NP due to historical lack of efficient solutions for longstanding mathematical problems.']}, {'end': 4368.657, 'segs': [{'end': 3213.282, 'src': 'embed', 'start': 3185.919, 'weight': 5, 'content': [{'end': 3199.632, 'text': 'But once you have found the factors, expressed the number as a product to smaller numbers, you can quickly verify that they are factors of the number.', 'start': 3185.919, 'duration': 13.713}, {'end': 3206.877, 'text': 'Your intuition is a lot of brilliant people have tried to find algorithms for this one particular problem.', 'start': 3200.053, 'duration': 6.824}, {'end': 3213.282, 'text': "There's many others like it that are really well studied and it would be great to find an efficient algorithm for.", 'start': 3206.917, 'duration': 6.365}], 'summary': 'Finding efficient algorithm for factoring numbers is a well-studied problem.', 'duration': 27.363, 'max_score': 3185.919, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs3185919.jpg'}, {'end': 3667.726, 'src': 'embed', 'start': 3633.242, 'weight': 4, 'content': [{'end': 3650.486, 'text': "So when I saw Cook's paper and saw this reduction of each of the problems in NP by a uniform method to the satisfiability problem of propositional logic,", 'start': 3633.242, 'duration': 17.244}, {'end': 3657.44, 'text': 'That meant that the satisfiability problem was a universal, combinatorial problem.', 'start': 3652.577, 'duration': 4.863}, {'end': 3667.726, 'text': 'And it occurred to me, through experience I had had in trying to solve other combinatorial problems,', 'start': 3659.441, 'duration': 8.285}], 'summary': "Cook's paper reduced np problems to propositional logic satisfiability, making it a universal combinatorial problem.", 'duration': 34.484, 'max_score': 3633.242, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs3633242.jpg'}, {'end': 3879.234, 'src': 'embed', 'start': 3847.128, 'weight': 9, 'content': [{'end': 3860.8, 'text': 'Now to satisfy all those clauses, you have to find one of the terms in each clause which is going to be true in your truth assignment,', 'start': 3847.128, 'duration': 13.672}, {'end': 3864.303, 'text': "but you can't make the same variable both true and false.", 'start': 3860.8, 'duration': 3.503}, {'end': 3874.291, 'text': 'So if you have the variable A in one clause and you want to satisfy that clause by making A true,', 'start': 3864.783, 'duration': 9.508}, {'end': 3879.234, 'text': "you can't also make the complement of a true in some other clause.", 'start': 3874.291, 'duration': 4.943}], 'summary': 'To satisfy all clauses, find one true term in each, avoiding same variable being true and false.', 'duration': 32.106, 'max_score': 3847.128, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs3847128.jpg'}, {'end': 3938.309, 'src': 'embed', 'start': 3901.149, 'weight': 6, 'content': [{'end': 3910.735, 'text': "where you're just sort of asking for a set of vertices in a graph such that no two of them are adjacent, sort of the opposite of the clique problem.", 'start': 3901.149, 'duration': 9.586}, {'end': 3932.907, 'text': "So we've seen that we can now express that as finding a set of terms, one in each clause,", 'start': 3915.018, 'duration': 17.889}, {'end': 3938.309, 'text': 'without picking both the variable and the negation of that variable.', 'start': 3932.907, 'duration': 5.402}], 'summary': 'Finding a set of non-adjacent vertices in a graph, opposite of the clique problem.', 'duration': 37.16, 'max_score': 3901.149, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs3901149.jpg'}, {'end': 4009.718, 'src': 'embed', 'start': 3984.286, 'weight': 0, 'content': [{'end': 3992.63, 'text': "and also an edge between them if they represent opposite values of the same variable, because you can't make a variable both true and false.", 'start': 3984.286, 'duration': 8.344}, {'end': 3997.812, 'text': 'And so you get a graph where you have all of these occurrences of variables.', 'start': 3993.37, 'duration': 4.442}, {'end': 4004.915, 'text': "You have edges which mean that you're not allowed to choose both ends of the edge,", 'start': 3998.172, 'duration': 6.743}, {'end': 4009.718, 'text': "either because they're in the same clause or they're negations of one another.", 'start': 4004.915, 'duration': 4.803}], 'summary': 'Graph represents variables and edges, prohibits choosing opposite values.', 'duration': 25.432, 'max_score': 3984.286, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs3984286.jpg'}, {'end': 4190.733, 'src': 'embed', 'start': 4160.3, 'weight': 7, 'content': [{'end': 4166.863, 'text': "There is a clique of size 15 or there's not a clique of size 15.", 'start': 4160.3, 'duration': 6.563}, {'end': 4172.385, 'text': 'On the other hand, an optimization problem would be asking, find the largest clique.', 'start': 4166.863, 'duration': 5.522}, {'end': 4177.488, 'text': 'The answer would not be yes or no, it would be 15.', 'start': 4173.145, 'duration': 4.343}, {'end': 4189.073, 'text': "So when you're putting a valuation on the different solutions and you're asking for the one with the highest valuation,", 'start': 4177.488, 'duration': 11.585}, {'end': 4190.733, 'text': "that's an optimization problem.", 'start': 4189.073, 'duration': 1.66}], 'summary': 'An optimization problem aims to find the largest clique, which would be of size 15.', 'duration': 30.433, 'max_score': 4160.3, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs4160300.jpg'}, {'end': 4335.872, 'src': 'embed', 'start': 4309.283, 'weight': 3, 'content': [{'end': 4319.549, 'text': 'If P is unequal to NP, which is what we expect, then we know that for the great majority of the combinatorial problems that come up,', 'start': 4309.283, 'duration': 10.266}, {'end': 4326.83, 'text': "since they're known to be NP-complete, we're not going to be able to solve them by efficient algorithms.", 'start': 4319.549, 'duration': 7.281}, {'end': 4335.872, 'text': "However, there's a little bit of hope in that it may be that we can solve most instances.", 'start': 4327.87, 'duration': 8.002}], 'summary': 'If p ≠ np, then most combinatorial problems are unsolvable by efficient algorithms, but some instances may be solvable.', 'duration': 26.589, 'max_score': 4309.283, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs4309283.jpg'}], 'start': 3185.919, 'title': 'Complexity theory and np problems', 'summary': 'Explores the significance of efficient algorithms for np problems, the implications of p equals np, and the connections between combinatorial problems, computational complexity, and the potential impact of proving p equals np or p not equals np, with references to the satisfiability problem, universal computation, and reductions.', 'chapters': [{'end': 3415.192, 'start': 3185.919, 'title': 'Efficiency of algorithms in np problems', 'summary': 'Discusses the importance of finding efficient algorithms for problems within the class np, and the potential implications of p being equal to np, with reference to the satisfiability problem of propositional logic and its tie to other combinatorial problems.', 'duration': 229.273, 'highlights': ['The chapter discusses the importance of finding efficient algorithms for problems within the class NP Efficient algorithms for NP problems are a focal point, with implications for the broader field of computer science.', 'The potential implications of P being equal to NP, with reference to the satisfiability problem of propositional logic and its tie to other combinatorial problems P being equal to NP could lead to significant implications, such as the potential for efficient solutions to a wide range of combinatorial problems.', 'The importance of the satisfiability problem of propositional logic The satisfiability problem serves as a fundamental and challenging problem in computer science, representing a key aspect of NP problems.', "Stephen Cook's result that every problem in NP can be re-expressed as an instance of the satisfiability problem Cook's result demonstrates the foundational link between NP problems and the satisfiability problem, showcasing its significance in the broader context of computational complexity."]}, {'end': 3759.171, 'start': 3416.373, 'title': 'Universal computation and reductions', 'summary': 'Discusses the concept of turing machines as a universal computation model and their use in representing all possible computation, leading to the astonishing implication that all problems in p can be rewritten in terms of the satisfiability problem, thus adding weight to the p equals np question.', 'duration': 342.798, 'highlights': ['Turing machines can be used to describe any algorithm, representing all possible computation. The Turing machine can be used to describe any algorithm, thus representing all possible computation.', 'All problems in P can be rewritten in terms of the satisfiability problem. The astonishing implication that all problems in P can be rewritten in terms of the satisfiability problem.', 'The satisfiability problem can be restated as an integer programming problem, making the problem much harder. The satisfiability problem can be restated as an integer programming problem, which makes the problem much harder.']}, {'end': 4368.657, 'start': 3763.085, 'title': 'Reduction of propositional logic to graph theory', 'summary': 'Discusses the reduction of the propositional logic problem to the independent set problem in graph theory, showing the connection between combinatorial algorithms and computational complexity, and the potential impact of proving p equals np or p not equals np.', 'duration': 605.572, 'highlights': ['The propositional logic problem can be expressed as a number of clauses, and the satisfiability problem aims to find if those clauses can be simultaneously satisfied. The propositional logic problem is expressed as a set of clauses, and the satisfiability problem seeks to determine if these clauses can be satisfied simultaneously.', 'The reduction of the propositional logic problem to the independent set problem in graph theory is discussed, connecting the two problems through the representation of clauses and terms as vertices and edges in a graph. The reduction of the propositional logic problem to the independent set problem in graph theory is explained, demonstrating the connection between the two problems through the representation of clauses and terms as vertices and edges in a graph.', 'The potential impact of proving P equals NP or P not equals NP on theoretical computer science and software-based systems is discussed, emphasizing the enormous impact it would have on the world in either case. The potential impact of proving P equals NP or P not equals NP on theoretical computer science and software-based systems is highlighted, stressing the significant implications it would have on the world.']}], 'duration': 1182.738, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs3185919.jpg', 'highlights': ['Efficient algorithms for NP problems are crucial, with broader implications for computer science.', 'P being equal to NP could lead to significant implications, such as efficient solutions to combinatorial problems.', 'The satisfiability problem is fundamental and challenging, representing a key aspect of NP problems.', "Stephen Cook's result demonstrates the foundational link between NP problems and the satisfiability problem.", 'Turing machines can describe any algorithm, representing all possible computation.', 'All problems in P can be rewritten in terms of the satisfiability problem, an astonishing implication.', 'Restating the satisfiability problem as an integer programming problem makes it much harder.', 'The satisfiability problem seeks to determine if clauses can be satisfied simultaneously.', 'The reduction of the propositional logic problem to the independent set problem in graph theory is explained.', 'The potential impact of proving P equals NP or P not equals NP on theoretical computer science and software-based systems is discussed.']}, {'end': 4831.271, 'segs': [{'end': 4437.26, 'src': 'embed', 'start': 4395.512, 'weight': 1, 'content': [{'end': 4402.041, 'text': 'I like the stable matching problem, or the stable marriage problem, very much.', 'start': 4395.512, 'duration': 6.529}, {'end': 4413.696, 'text': "What's the stable matching problem? Imagine that you want to marry off n boys with n girls.", 'start': 4402.902, 'duration': 10.794}, {'end': 4425.992, 'text': 'And each boy has an ordered list of his preferences among the girls, his first choice, his second choice, through her nth choice.', 'start': 4417.365, 'duration': 8.627}, {'end': 4437.26, 'text': 'And each girl also has an ordering of the boys, first choice, second choice, and so on.', 'start': 4427.633, 'duration': 9.627}], 'summary': 'Stable matching problem involves pairing n boys with n girls based on ordered preferences.', 'duration': 41.748, 'max_score': 4395.512, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs4395512.jpg'}, {'end': 4747.993, 'src': 'embed', 'start': 4696.165, 'weight': 0, 'content': [{'end': 4699.328, 'text': 'Why is it a problem for the husband and wife to be assigned to the same hospital?', 'start': 4696.165, 'duration': 3.163}, {'end': 4702.503, 'text': "No, it's desirable.", 'start': 4700.04, 'duration': 2.463}, {'end': 4709.351, 'text': "or at least go to the same city if you're assigning residents to hospitals.", 'start': 4702.503, 'duration': 6.848}, {'end': 4716.74, 'text': 'And then you have some preferences for the husband and the wife or for the hospitals? The residents have their own preferences.', 'start': 4709.591, 'duration': 7.149}, {'end': 4722.896, 'text': 'Residents, both male and female, have their own preferences.', 'start': 4719.028, 'duration': 3.868}, {'end': 4726.663, 'text': 'The hospitals have their preferences.', 'start': 4724.779, 'duration': 1.884}, {'end': 4744.23, 'text': "But if resident A, the boy, is going to Philadelphia, then you'd like his wife also to be assigned to a hospital in Philadelphia.", 'start': 4727.745, 'duration': 16.485}, {'end': 4747.993, 'text': 'Which step makes it a NP-hard problem that you mentioned?', 'start': 4744.49, 'duration': 3.503}], 'summary': 'Assigning husband and wife residents to same city hospital preferences causing np-hard problem.', 'duration': 51.828, 'max_score': 4696.165, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs4696165.jpg'}], 'start': 4368.657, 'title': 'Stable matching problem', 'summary': 'Discusses the stable matching problem, a combinatorial algorithm used to match n boys with n girls, ensuring a stable one-to-one matching without any pair wanting to abscond from each other. it also explains the complexity of the problem when considering constraints such as assigning husband and wife to the same hospital, making it np-hard. additionally, it highlights the historical significance of the algorithm by gale and shapley in the context of a nobel prize in economics.', 'chapters': [{'end': 4667.896, 'start': 4368.657, 'title': 'Stable matching problem', 'summary': 'Discusses the stable matching problem, a combinatorial algorithm used to match n boys with n girls, ensuring a stable one-to-one matching without any pair wanting to abscond from each other, with relevance to real-life problems and a lesson for the boys to be proactive.', 'duration': 299.239, 'highlights': ['The stable matching problem ensures a one-to-one matching of boys with girls without any pair wanting to abscond from each other, with relevance to real-life problems like matching residence with hospitals. The stable matching problem ensures a one-to-one matching of boys with girls without any pair wanting to abscond from each other, with relevance to real-life problems like matching residence with hospitals.', 'A stable matching exists for any set of preferences, and it can be computed by a simple algorithm where each boy starts making proposals to girls, and if a girl receives a proposal, she accepts it tentatively, but can drop it later if she gets a better proposal, with the boys never going back through the list. A stable matching exists for any set of preferences, and it can be computed by a simple algorithm where each boy starts making proposals to girls, and if a girl receives a proposal, she accepts it tentatively, but can drop it later if she gets a better proposal, with the boys never going back through the list.', "The algorithm ensures that the boys are doing at least as well as they could do in any other stable matching, conveying a lesson for the boys to be proactive and make proposals, with the observation that it's the boys who are doing the best. The algorithm ensures that the boys are doing at least as well as they could do in any other stable matching, conveying a lesson for the boys to be proactive and make proposals, with the observation that it's the boys who are doing the best."]}, {'end': 4831.271, 'start': 4669.137, 'title': 'Stable matching problem explained', 'summary': 'Explains the stable matching problem, highlighting the complexity when considering constraints such as assigning husband and wife to the same hospital, with an additional constraint making it np-hard, and the historical significance of the algorithm by gale and shapley in the context of a nobel prize in economics.', 'duration': 162.134, 'highlights': ['The problem becomes NP-hard when considering the constraint of having both partners to a marriage assigned to the same place. The additional constraint of assigning both partners of a marriage to the same place increases the complexity of the stable matching problem to NP-hard.', 'The algorithm by Gale and Shapley, addressing stable matching, led to a Nobel Prize in Economics. The algorithm developed by Gale and Shapley for stable matching contributed to a Nobel Prize in Economics, with Shapley being recognized for his work after his partner, David Gale, passed away.', 'The desire for husband and wife to be assigned to the same hospital or city adds complexity to the stable matching problem. The preference for assigning both partners of a marriage to the same hospital or city introduces a desirable constraint that contributes to the complexity of the stable matching problem.']}], 'duration': 462.614, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs4368657.jpg', 'highlights': ['The algorithm by Gale and Shapley, addressing stable matching, led to a Nobel Prize in Economics.', 'The preference for assigning both partners of a marriage to the same hospital or city introduces a desirable constraint that contributes to the complexity of the stable matching problem.', 'The additional constraint of assigning both partners of a marriage to the same place increases the complexity of the stable matching problem to NP-hard.', 'A stable matching exists for any set of preferences, and it can be computed by a simple algorithm where each boy starts making proposals to girls, and if a girl receives a proposal, she accepts it tentatively, but can drop it later if she gets a better proposal, with the boys never going back through the list.']}, {'end': 5523.768, 'segs': [{'end': 5186.854, 'src': 'embed', 'start': 5160.81, 'weight': 0, 'content': [{'end': 5165.671, 'text': 'And if it was of substantial size, say a few thousand,', 'start': 5160.81, 'duration': 4.861}, {'end': 5174.493, 'text': 'then the most popular candidate in that group would be very likely to be the correct choice that would come out of counting all the millions of votes.', 'start': 5165.671, 'duration': 8.822}, {'end': 5180.929, 'text': "Now, of course, we can't do this because, first of all, everybody has to feel that his or her vote counted.", 'start': 5176.203, 'duration': 4.726}, {'end': 5186.854, 'text': "And secondly, we can't really do a purely random sample from that population.", 'start': 5181.912, 'duration': 4.942}], 'summary': "A few thousand votes could predict the most popular candidate, but it's not feasible due to the need for every vote to count and the challenge of a purely random sample.", 'duration': 26.044, 'max_score': 5160.81, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs5160810.jpg'}, {'end': 5375.027, 'src': 'heatmap', 'start': 5272.532, 'weight': 1, 'content': [{'end': 5294.376, 'text': "And you can show that suitably define the, the probability that you will get a violation of Fermat's result is very high,", 'start': 5272.532, 'duration': 21.844}, {'end': 5299.799, 'text': 'and so this gives you a way of rapidly proving that a number is not prime.', 'start': 5294.376, 'duration': 5.423}, {'end': 5308.604, 'text': "It's a little more complicated than that, because there are certain values of n where something a little more elaborate has to be done,", 'start': 5301.079, 'duration': 7.525}, {'end': 5309.904, 'text': "but that's the basic idea.", 'start': 5308.604, 'duration': 1.3}, {'end': 5323.391, 'text': 'Taking an identity that holds for primes and therefore, if it ever fails on any instance for a non-prime, you know that the number is not prime.', 'start': 5312.606, 'duration': 10.785}, {'end': 5327.513, 'text': "It's a quick choice, a fast choice, fast proof that a number is not prime.", 'start': 5323.451, 'duration': 4.062}, {'end': 5336.131, 'text': "Can you maybe elaborate a little bit more of what's your intuition, why randomness works so well and results in such simple algorithms?", 'start': 5328.769, 'duration': 7.362}, {'end': 5343.193, 'text': 'Well, the example of conducting an election, where in theory,', 'start': 5337.592, 'duration': 5.601}, {'end': 5352.056, 'text': 'you could take a sample and depend on the validity of the sample to really represent the whole, is just the basic fact of statistics,', 'start': 5343.193, 'duration': 8.863}, {'end': 5354.516, 'text': 'which gives a lot of opportunities.', 'start': 5352.056, 'duration': 2.46}, {'end': 5375.027, 'text': 'And I actually exploited that sort of random sampling idea in designing an algorithm for counting the number of solutions that satisfy a particular formula and propositional logic.', 'start': 5357.936, 'duration': 17.091}], 'summary': 'Using randomness and statistics for fast prime number testing and algorithm design.', 'duration': 102.495, 'max_score': 5272.532, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs5272532.jpg'}, {'end': 5523.768, 'src': 'embed', 'start': 5491.716, 'weight': 1, 'content': [{'end': 5494.597, 'text': 'If a row has more 1s, it gets drawn more frequently.', 'start': 5491.716, 'duration': 2.881}, {'end': 5499.888, 'text': 'But then, if you draw from that row,', 'start': 5496.004, 'duration': 3.884}, {'end': 5514.102, 'text': "you have to go up the column and looking at where that same one is repeated in different rows and only count it as a success or a hit if it's the earliest row that contains the one.", 'start': 5499.888, 'duration': 14.214}, {'end': 5523.768, 'text': 'Right And that gives you a robust statistical estimate of the total number of columns that contain at least one of the ones.', 'start': 5514.122, 'duration': 9.646}], 'summary': 'Drawing from rows with more 1s gives statistical estimate of columns with at least one 1.', 'duration': 32.052, 'max_score': 5491.716, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs5491716.jpg'}], 'start': 4832.631, 'title': 'Randomized algorithms', 'summary': "Covers the rabin-karp algorithm for string searching pattern matching using random prime numbers, emphasizing the power of randomization, and discusses fermat's little theorem and random sampling in algorithm design, highlighting the effectiveness of randomness.", 'chapters': [{'end': 5210.285, 'start': 4832.631, 'title': 'Rabin-karp algorithm: power of randomization', 'summary': 'Discusses the rabin-karp algorithm for string searching pattern matching, illustrating the power of randomization in achieving efficient string matching, using random prime numbers as hash functions to compute fingerprints, offering simplicity in computation and low probability of error.', 'duration': 377.654, 'highlights': ['The Rabin-Karp algorithm uses random prime numbers as hash functions to compute fingerprints, enabling simple computation of fingerprints and ensuring a low probability of error.', 'The algorithm leverages the power of randomization to efficiently search for a given word within a much longer word, demonstrating the effectiveness of adding randomness to achieve a naive yet highly efficient approach.', 'Randomized algorithms, like the Rabin-Karp algorithm, utilize the ability to draw random numbers from a range or associate random numbers with objects, showcasing the potential of randomness in algorithm design and execution.', 'The concept of randomized algorithms is illustrated by the example of conducting a presidential election, where drawing a random sample of voters could potentially determine the most popular candidate with a low probability of error, highlighting the potential of random selection in problem-solving.']}, {'end': 5523.768, 'start': 5211.383, 'title': "Fermat's little theorem and random sampling", 'summary': "Discusses fermat's little theorem as a method to rapidly prove a number is not prime, and the use of random sampling in designing algorithms for counting solutions, providing insights into the effectiveness of randomness in algorithms.", 'duration': 312.385, 'highlights': ["Fermat's Little Theorem provides a method to rapidly prove a number is not prime by checking if raising a number to the power of n-minus-1 modulo n results in the original number, with high probability of detecting non-prime numbers. Method to rapidly prove a number is not prime, using n-minus-1th power modulo n, high probability of detecting non-prime numbers.", 'Random sampling is effective in algorithm design, as demonstrated in the use of random sampling to count solutions satisfying particular formulas in propositional logic, preventing double counting and providing a robust statistical estimate of the total number of solutions. Effectiveness of random sampling in algorithm design, preventing double counting, robust statistical estimate of solutions.']}], 'duration': 691.137, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs4832631.jpg', 'highlights': ['The Rabin-Karp algorithm uses random prime numbers as hash functions to compute fingerprints, ensuring a low probability of error.', 'Randomized algorithms, like the Rabin-Karp algorithm, utilize the ability to draw random numbers from a range, showcasing the potential of randomness in algorithm design and execution.', 'The algorithm leverages the power of randomization to efficiently search for a given word within a much longer word, demonstrating the effectiveness of adding randomness to achieve a naive yet highly efficient approach.', 'The concept of randomized algorithms is illustrated by the example of conducting a presidential election, where drawing a random sample of voters could potentially determine the most popular candidate with a low probability of error.']}, {'end': 7643.484, 'segs': [{'end': 5616.932, 'src': 'embed', 'start': 5592.732, 'weight': 8, 'content': [{'end': 5601.559, 'text': 'If there are many ways for the two to disagree, and you only need to find one disagreement, then random choice is likely to yield it.', 'start': 5592.732, 'duration': 8.827}, {'end': 5603.581, 'text': 'And in general.', 'start': 5602.66, 'duration': 0.921}, {'end': 5609.766, 'text': "so we've just talked about randomized algorithms, but we can look at the probabilistic analysis of algorithms,", 'start': 5603.581, 'duration': 6.185}, {'end': 5616.932, 'text': "and that gives us an opportunity to step back and, as we've said, everything we've been talking about is worst-case analysis.", 'start': 5609.766, 'duration': 7.166}], 'summary': 'Randomized algorithms offer opportunity for probabilistic analysis of worst-case scenarios.', 'duration': 24.2, 'max_score': 5592.732, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs5592732.jpg'}, {'end': 5761.478, 'src': 'embed', 'start': 5700.18, 'weight': 6, 'content': [{'end': 5703.281, 'text': 'There are very powerful programs called SAT solvers,', 'start': 5700.18, 'duration': 3.101}, {'end': 5717.491, 'text': 'which in practice fairly reliably solve instances with many millions of variables that arise in digital design or in proving programs correct in other applications.', 'start': 5704.541, 'duration': 12.95}, {'end': 5724.534, 'text': 'And so in many application areas.', 'start': 5720.272, 'duration': 4.262}, {'end': 5731.037, 'text': "even though satisfiability, as we've already discussed, is NP-complete,", 'start': 5724.534, 'duration': 6.503}, {'end': 5739.842, 'text': 'the SAT solvers will work so well that the people in that discipline tend to think of satisfiability as an easy problem.', 'start': 5731.037, 'duration': 8.805}, {'end': 5746.907, 'text': "So in other words, just for some reason that we don't entirely understand.", 'start': 5741.203, 'duration': 5.704}, {'end': 5761.478, 'text': 'the instances that people formulate in designing digital circuits or other applications are such that satisfiability is not hard to check.', 'start': 5746.907, 'duration': 14.571}], 'summary': 'Sat solvers reliably solve instances with millions of variables in digital design and program correctness, making satisfiability seem easy despite being np-complete.', 'duration': 61.298, 'max_score': 5700.18, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs5700180.jpg'}, {'end': 6205.395, 'src': 'embed', 'start': 6178.846, 'weight': 10, 'content': [{'end': 6185.868, 'text': "and be respected, and at the same time, be respected in the theoretical computer science community? That hasn't been achieved yet, I'm afraid.", 'start': 6178.846, 'duration': 7.022}, {'end': 6189.049, 'text': 'Is that P equals NP?', 'start': 6186.349, 'duration': 2.7}, {'end': 6189.97, 'text': 'Is that impossible?', 'start': 6189.089, 'duration': 0.881}, {'end': 6202.814, 'text': 'Is it impossible to publish a successful paper in the theoretical computer science community that shows some performance on a real-world dataset?', 'start': 6191.87, 'duration': 10.944}, {'end': 6204.335, 'text': 'Or is that really just?', 'start': 6203.254, 'duration': 1.081}, {'end': 6205.395, 'text': 'those are two different worlds?', 'start': 6204.335, 'duration': 1.06}], 'summary': 'Challenges in achieving respect and success in theoretical computer science community.', 'duration': 26.549, 'max_score': 6178.846, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs6178846.jpg'}, {'end': 6352.101, 'src': 'embed', 'start': 6322.162, 'weight': 3, 'content': [{'end': 6330.087, 'text': 'In other words, briefly, what you would say in that case is that the problem has small circuits, polynomial-sized circuits.', 'start': 6322.162, 'duration': 7.925}, {'end': 6338.836, 'text': 'Now we know that if P is equal to NP, then in fact these problems will have small circuits.', 'start': 6332.694, 'duration': 6.142}, {'end': 6340.977, 'text': 'But what about the converse??', 'start': 6339.717, 'duration': 1.26}, {'end': 6343.238, 'text': 'Could a problem have small circuits,', 'start': 6341.377, 'duration': 1.861}, {'end': 6352.101, 'text': 'meaning that an algorithm tailored to any particular size could work well and yet not be a polynomial time algorithm??', 'start': 6343.238, 'duration': 8.863}], 'summary': 'Small circuits imply polynomial-sized circuits, which may not be polynomial time algorithm.', 'duration': 29.939, 'max_score': 6322.162, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs6322162.jpg'}, {'end': 6606.476, 'src': 'embed', 'start': 6572.515, 'weight': 17, 'content': [{'end': 6573.915, 'text': 'Harder and harder to solve.', 'start': 6572.515, 'duration': 1.4}, {'end': 6585.229, 'text': 'And what Lifton and I showed was that if NP had small circuits, then this hierarchy would collapse down to the second level.', 'start': 6575.578, 'duration': 9.651}, {'end': 6593.377, 'text': "In other words, you wouldn't get any more mileage by complicating your expressions with three quantifiers or four quantifiers or any number.", 'start': 6586.37, 'duration': 7.007}, {'end': 6597.522, 'text': "I'm not sure what to make of that exactly.", 'start': 6595.56, 'duration': 1.962}, {'end': 6606.476, 'text': "Well, I think it would be evidence that NP doesn't have small circuits, because something so bizarre would happen.", 'start': 6597.924, 'duration': 8.552}], 'summary': 'If np had small circuits, the hierarchy would collapse down to the second level.', 'duration': 33.961, 'max_score': 6572.515, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs6572515.jpg'}, {'end': 6855.719, 'src': 'embed', 'start': 6800.062, 'weight': 13, 'content': [{'end': 6813.83, 'text': 'So yeah, they may seem to work on your training set, and you may be able to discover whether your photos occur in a different sample of inputs or not.', 'start': 6800.062, 'duration': 13.768}, {'end': 6817.472, 'text': "But we don't really know what's going on.", 'start': 6815.731, 'duration': 1.741}, {'end': 6827.457, 'text': "We don't know the features that distinguish the photographs or the objects are not easy to characterize.", 'start': 6817.532, 'duration': 9.925}, {'end': 6835.922, 'text': "Well, it's interesting because you mentioned coming up with a small circuit to solve a particular size problem.", 'start': 6829.618, 'duration': 6.304}, {'end': 6839.444, 'text': 'It seems that neural networks are kind of small circuits.', 'start': 6836.442, 'duration': 3.002}, {'end': 6841.315, 'text': 'In a way, yeah.', 'start': 6840.015, 'duration': 1.3}, {'end': 6842.516, 'text': "But they're not programs.", 'start': 6841.375, 'duration': 1.141}, {'end': 6846.337, 'text': "Sort of like the things you've designed are algorithms, programs.", 'start': 6842.856, 'duration': 3.481}, {'end': 6848.157, 'text': 'Right Algorithms.', 'start': 6846.617, 'duration': 1.54}, {'end': 6853.619, 'text': "Neural networks aren't able to develop algorithms to solve a problem.", 'start': 6848.997, 'duration': 4.622}, {'end': 6855.719, 'text': "It's more of a function.", 'start': 6854.239, 'duration': 1.48}], 'summary': 'Challenges in understanding features of neural networks and their limitations in developing algorithms.', 'duration': 55.657, 'max_score': 6800.062, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs6800062.jpg'}, {'end': 7378.109, 'src': 'embed', 'start': 7335.719, 'weight': 5, 'content': [{'end': 7352.657, 'text': 'And when they talked about me, they talked not about my 1979 paper or 1992 paper, but about what came away in my classes.', 'start': 7335.719, 'duration': 16.938}, {'end': 7359.099, 'text': 'And not just the details, but just the approach and the manner of teaching.', 'start': 7353.618, 'duration': 5.481}, {'end': 7362.48, 'text': 'And so I sort of take pride.', 'start': 7360.419, 'duration': 2.061}, {'end': 7367.821, 'text': 'at least in my early years as a faculty member at Berkeley,', 'start': 7362.48, 'duration': 5.341}, {'end': 7378.109, 'text': 'I was exemplary in preparing my lectures and I always came in prepared to the teeth and able, therefore,', 'start': 7367.821, 'duration': 10.288}], 'summary': 'Exemplary teaching at berkeley focused on approach and preparation.', 'duration': 42.39, 'max_score': 7335.719, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs7335719.jpg'}, {'end': 7425.782, 'src': 'embed', 'start': 7400.368, 'weight': 0, 'content': [{'end': 7408.117, 'text': 'But are there other things, pieces of advice that you can impart? Well, the top three would be preparation, preparation, and preparation.', 'start': 7400.368, 'duration': 7.749}, {'end': 7419.781, 'text': "Why is preparation so important, I guess? It's because it gives you the ease to deal with any situation that comes up in the classroom.", 'start': 7409.778, 'duration': 10.003}, {'end': 7425.782, 'text': "If you discover that you're not getting through one way, you can do it another way.", 'start': 7419.801, 'duration': 5.981}], 'summary': 'Top three pieces of advice: preparation, preparation, preparation for dealing with classroom situations.', 'duration': 25.414, 'max_score': 7400.368, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs7400368.jpg'}, {'end': 7589.188, 'src': 'embed', 'start': 7560.831, 'weight': 2, 'content': [{'end': 7565.733, 'text': 'And it made me realize that I had some ability that was going somewhere.', 'start': 7560.831, 'duration': 4.902}, {'end': 7570.843, 'text': "You realize you're pretty good at this thing.", 'start': 7569.182, 'duration': 1.661}, {'end': 7574.266, 'text': "I don't think there's a better way to end it, Richard.", 'start': 7572.385, 'duration': 1.881}, {'end': 7575.187, 'text': 'It was a huge honor.', 'start': 7574.286, 'duration': 0.901}, {'end': 7577.908, 'text': 'Thank you for decades of incredible work.', 'start': 7575.287, 'duration': 2.621}, {'end': 7579.029, 'text': 'Thank you for talking today.', 'start': 7578.269, 'duration': 0.76}, {'end': 7579.269, 'text': 'Thank you.', 'start': 7579.049, 'duration': 0.22}, {'end': 7580.31, 'text': "It's been a great pleasure.", 'start': 7579.309, 'duration': 1.001}, {'end': 7583.512, 'text': "You're a superb interviewer.", 'start': 7580.851, 'duration': 2.661}, {'end': 7585.574, 'text': "I'll stop it.", 'start': 7584.513, 'duration': 1.061}, {'end': 7589.188, 'text': 'Thanks for listening to this conversation with Richard Karp.', 'start': 7586.786, 'duration': 2.402}], 'summary': "Acknowledging richard karp's decades of incredible work and expressing gratitude for the conversation.", 'duration': 28.357, 'max_score': 7560.831, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs7560831.jpg'}, {'end': 7643.484, 'src': 'embed', 'start': 7608.363, 'weight': 1, 'content': [{'end': 7615.428, 'text': 'even just visiting the site, but also considering the purchase, helps them know that this podcast is worth supporting in the future.', 'start': 7608.363, 'duration': 7.065}, {'end': 7618.831, 'text': "It really is the best way to support this journey I'm on.", 'start': 7615.948, 'duration': 2.883}, {'end': 7625.556, 'text': 'If you enjoy this thing, subscribe on YouTube, review it with five stars on Apple Podcasts, support it on Patreon.', 'start': 7619.731, 'duration': 5.825}, {'end': 7630.459, 'text': 'connect with me on Twitter at Lex Friedman, if you can figure out how to spell that.', 'start': 7625.556, 'duration': 4.903}, {'end': 7635.007, 'text': 'And now let me leave you with some words from Isaac Asimov.', 'start': 7631.42, 'duration': 3.587}, {'end': 7637.352, 'text': 'I do not fear computers.', 'start': 7636.089, 'duration': 1.263}, {'end': 7639.556, 'text': 'I fear lack of them.', 'start': 7638.274, 'duration': 1.282}, {'end': 7643.484, 'text': 'Thank you for listening and hope to see you next time.', 'start': 7640.819, 'duration': 2.665}], 'summary': "Visiting and supporting the podcast site aids future backing. subscribing on youtube, giving a five-star review on apple podcasts, and supporting on patreon are ways to help. connect with the host on twitter at lex friedman. isaac asimov's words: 'i do not fear computers. i fear lack of them.'", 'duration': 35.121, 'max_score': 7608.363, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs7608363.jpg'}], 'start': 5524.609, 'title': 'Algorithm analysis and applications', 'summary': "Covers topics including randomized algorithms, worst-case analysis, np-hard problems, challenges in algorithm performance analysis, complexity theory, small circuits for np problems, np hierarchy collapse, limitations in machine learning, gene editing, algorithms in bioinformatics, and richard karp's teaching and research.", 'chapters': [{'end': 5847.581, 'start': 5524.609, 'title': 'Randomized algorithms and probabilistic analysis', 'summary': 'Discusses the application of random sampling in solving algebraic identities, the power of worst-case analysis in judging algorithms, and the practical efficiency of algorithms for np-hard problems such as satisfiability and the traveling salesman problem.', 'duration': 322.972, 'highlights': ['The application of random sampling in solving algebraic identities and evaluating distinct formulas. Random sampling is used to evaluate algebraic identities and distinct formulas by picking a random value and checking if they agree, relying on the fact that distinct formulas will exhibit disagreement.', 'The practical efficiency of algorithms for NP-hard problems such as satisfiability and the traveling salesman problem. Despite NP-hardness, algorithms such as SAT solvers and integer programming codes efficiently solve instances of problems like satisfiability and the traveling salesman problem in practice, even for large problem sizes.', "The power of worst-case analysis in judging algorithms and the need to consider average case analysis. Worst-case analysis is important in judging algorithms, but it's also crucial to consider average case analysis to understand how often a good solution can be obtained."]}, {'end': 6270.644, 'start': 5848.622, 'title': 'Challenges in algorithm performance analysis', 'summary': 'Discusses the challenges in algorithm performance analysis, including the difficulty in defining typical instances, the lack of representative real-world datasets for analysis, and the disconnect between theoretical computer science and empirical analysis. it also highlights the limitations of average case analysis and the need for defining meaningful classes of graphs for practical application.', 'duration': 422.022, 'highlights': ['The average case analysis and understanding typical instances of problems are difficult, making it challenging to shed positive light on combinatorial algorithms. The speaker discusses the difficulty in understanding typical instances of problems and the challenges of average case analysis, highlighting the complexity of shedding positive light on combinatorial algorithms.', "The simplistic assumptions made in studying problems' behavior on the average or with high probability led to lukewarm acceptance of the results by the community. The speaker reflects on the lukewarm acceptance of results due to simplistic assumptions made in studying problems' behavior on the average or with high probability, impacting the practical application of the findings.", 'The lack of representative, real-world datasets for algorithm performance analysis poses a significant challenge in the field of complexity analysis, unlike in the machine learning world. The discussion emphasizes the absence of representative, real-world datasets for algorithm performance analysis in the complexity analysis field, unlike in the machine learning world, posing a significant challenge.', 'Defining meaningful classes of graphs for practical application is crucial, but the act of defining such classes is non-trivial when considering instances relevant to the real world. The importance of defining meaningful classes of graphs for practical application is highlighted, emphasizing the non-trivial nature of defining such classes when considering instances relevant to the real world.', 'The disconnect between theoretical computer science and empirical analysis hinders the use of real-world datasets for algorithm performance analysis and prevents the convergence of the two worlds. The chapter discusses the disconnect between theoretical computer science and empirical analysis, highlighting how it hinders the use of real-world datasets for algorithm performance analysis and prevents the convergence of the two worlds.']}, {'end': 6504.362, 'start': 6274.605, 'title': 'Complexity theory and small circuits', 'summary': 'Discusses the concept of small circuits for np problems, questioning whether problems could have small circuits without being polynomial time algorithms and contemplating the implications on complexity theory, with a focus on the existential question of whether the hamiltonian circuit problem has a small circuit for every size, even if p is not equal to np.', 'duration': 229.757, 'highlights': ['The chapter discusses the concept of small circuits for NP problems and questions if problems could have small circuits without being polynomial time algorithms. ', 'The existential question of whether the Hamiltonian circuit problem has a small circuit for every size is raised, even if P is not equal to NP. ', 'It is mentioned that if P is equal to NP, then problems will have small circuits, but the converse is also considered. ', 'The concept of a hierarchy in complexity theory, where the first level is P and the second level is NP, is briefly described. ']}, {'end': 6986.052, 'start': 6506.374, 'title': 'Np hierarchy collapse and machine learning limitations', 'summary': 'Discusses the collapse of the np hierarchy if np had small circuits, leading to limitations of theoretical understanding in machine learning, where neural networks perform well empirically but lack theoretical insight and interpretability.', 'duration': 479.678, 'highlights': ['The collapse of the NP hierarchy would occur if NP had small circuits, resulting in no additional complexity with more quantifiers.', 'Theoretical understanding in machine learning is limited as neural networks perform well empirically without clear theoretical understanding or interpretability.', 'Successes in machine learning have been observed in image processing, robotics, and game playing, leading to high demand and lucrative opportunities in the field.', 'Supervised learning problems through convolutional neural networks perform well even for inputs outside the training set, but there is no theoretical understanding of why this is true.', 'Neural networks lack clear interpretability as the features that distinguish photographs or objects are not easily characterized or understood.']}, {'end': 7221.176, 'start': 6986.733, 'title': 'Gene editing and algorithms in bioinformatics', 'summary': 'Discusses the fascinating aspects of gene editing and the ethical challenges it poses, along with the potential of algorithms to analyze genomic data and its impact on biological systems.', 'duration': 234.443, 'highlights': ['The ability to edit DNA is taking our biological system towards the world of algorithms, raising ethical questions and potential benefits in agriculture and medicine. The discussion highlights the fascinating ability to edit DNA, raising ethical questions and potential benefits in agriculture and medicine.', 'The ethical side of genetic engineering poses exceptional challenges, while algorithms offer potential benefits in modeling, optimizing, and studying biological systems. The ethical challenges of genetic engineering are emphasized, alongside the potential benefits of algorithms in modeling and studying biological systems.', 'The analysis of genomic data presents a significant big data problem, enabling the study of ancestry, disease tendencies, and personalized treatment based on genetic information. The significance of analyzing genomic data and its impact on studying ancestry, disease tendencies, and personalized treatment is emphasized as a big data problem.']}, {'end': 7643.484, 'start': 7224.372, 'title': "Richard karp's teaching and research", 'summary': "Delves into richard karp's teaching philosophy, emphasizing the importance of preparation, engaging with students individually, and the impact of a defining moment in his academic career.", 'duration': 419.112, 'highlights': ['Richard Karp emphasizes the importance of preparation as a teacher, ensuring the ability to adapt to any classroom situation and engage with students effectively. Preparation is crucial for dealing with any situation in the classroom and allows for flexibility in teaching methods. It enables the teacher to gauge student understanding and adjust the approach accordingly.', 'Karp discusses the individualized approach required for teaching, acknowledging that students have different learning styles and may need various forms of support and encouragement. Acknowledging the diversity of student needs, Karp emphasizes the importance of engaging with each student individually, understanding their strengths and weaknesses, and providing tailored support.', "Karp reflects on a pivotal moment in his academic career when he realized his potential through research and excelling in a mathematical methods course, leading to recognition from faculty. Karp's academic awakening came through research and excelling in a challenging course, which led to recognition from faculty and a realization of his abilities in the field of mathematics and operations research."]}], 'duration': 2118.875, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/KllCrlfLuzs/pics/KllCrlfLuzs5524609.jpg', 'highlights': ['Random sampling used to evaluate algebraic identities and distinct formulas.', 'Efficient algorithms for NP-hard problems like satisfiability and traveling salesman problem.', 'Importance of worst-case and average case analysis in judging algorithms.', 'Challenges in shedding positive light on combinatorial algorithms.', 'Impact of simplistic assumptions on the acceptance of results in the community.', 'Lack of representative real-world datasets for algorithm performance analysis.', 'Difficulty in defining meaningful classes of graphs for practical application.', 'Disconnect between theoretical computer science and empirical analysis.', 'Concept of small circuits for NP problems and their relation to polynomial time algorithms.', 'Existential question of whether the Hamiltonian circuit problem has a small circuit.', 'Hierarchy in complexity theory with P and NP as the first and second levels.', 'Potential collapse of the NP hierarchy if NP had small circuits.', 'Limited theoretical understanding in machine learning despite empirical success.', 'Successes and high demand in machine learning for image processing, robotics, and game playing.', 'Ethical questions and potential benefits of DNA editing in agriculture and medicine.', 'Challenges and potential benefits of genetic engineering and algorithms in biology.', 'Significance of analyzing genomic data for studying ancestry, disease tendencies, and personalized treatment.', 'Importance of preparation for effective teaching and flexibility in the classroom.', 'Individualized approach required for teaching to cater to diverse student needs.', "Karp's academic awakening through research and excelling in a mathematical methods course."]}], 'highlights': ["Karp's landmark paper proved 21 problems to be NP-complete, impacting the study of NP completeness and the P versus NP problem.", 'Richard Karp received the Turing Award in 1985 for his influential research in algorithms and complexity theory.', "The Admiralty-Karp algorithm and the Hopcroft-Karp algorithm are among Karp's influential algorithm developments.", 'The Eight Sleep Pod Pro mattress offers a $200 discount with temperature control down to 55 degrees on each side of the bed.', 'The mattress is equipped with sensors that track heart rate, heart rate variability, and respiratory rate, displaying the data in their app.', 'Cash App offers $10 when using the code LexPodcast, enabling users to send money, buy Bitcoin, and invest with as little as $1.', 'Michael Rabin provided an elegant solution for finding the shortest distance between two non-overlapping circles by using pure reasoning.', 'The proof that the sum of the angles of a triangle is 180 degrees was described as surprising and convincing.', 'The fascination with observing successive approaches to the optimum in solving problems like the traveling salesman problem.', 'The magic of algorithmic problem-solving, where the gap from the optimum decreases monotonically and various metrics improve until reaching the optimum.', 'The chapter delves into the assignment problem and the Hungarian algorithm, showcasing the aesthetic pleasure derived from contemplating the structure of computational processes.', 'The algorithm focuses on minimizing the sum of associated costs by subtracting constants from rows or columns in a matrix while maintaining non-negativity, leading to the optimal matching of sets.', 'The systematic and elegant nature of the iterative algorithm is found to be aesthetically pleasing, resonating with the satisfaction derived from shaping something into a beautiful and orderly form.', 'The chapter delves into the early history of computers, depicting the size and complexity of machines like the Mark IV and UNIVAC, providing a glimpse into the evolution of computing technology.', 'The discussion explores the skepticism towards achieving human-level intelligence through algorithms, emphasizing the limitations of current AI achievements in replicating human cognitive abilities and emotions.', 'The challenge of replicating consciousness and general intelligence in artificial intelligence is highlighted, expressing doubt about the singularity and the possibility of machines surpassing humans.', 'Development of a polynomial time algorithm for maximum flow problem, insights into algorithmic complexity and classes of algorithm complexity, focus on efficiency in large networks', 'Fundamental combinatorial problem of determining maximum flow rate, formal proof for solving maximum flow problem in polynomial time', 'Combinatorial algorithms deal with discrete objects and aim to minimize some cost function or prove the existence of a combinatorial configuration, as seen in examples like coloring the vertices of a graph', 'The class NP is introduced, consisting of problems hard to solve but verifiable in polynomial time, e.g., assignment problem with n cubed time complexity.', 'Importance of algorithms with poor worst-case performance yet high effectiveness is highlighted, focusing on problems solvable in polynomial time.', 'The satisfiability problem is fundamental and challenging, representing a key aspect of NP problems.', "Stephen Cook's result demonstrates the foundational link between NP problems and the satisfiability problem.", 'The algorithm by Gale and Shapley, addressing stable matching, led to a Nobel Prize in Economics.', 'The preference for assigning both partners of a marriage to the same hospital or city introduces a desirable constraint that contributes to the complexity of the stable matching problem.', 'The Rabin-Karp algorithm uses random prime numbers as hash functions to compute fingerprints, ensuring a low probability of error.', 'Randomized algorithms, like the Rabin-Karp algorithm, utilize the ability to draw random numbers from a range, showcasing the potential of randomness in algorithm design and execution.', 'Random sampling used to evaluate algebraic identities and distinct formulas.', 'Efficient algorithms for NP-hard problems like satisfiability and traveling salesman problem.', 'Importance of worst-case and average case analysis in judging algorithms.', 'Challenges in shedding positive light on combinatorial algorithms.', 'Impact of simplistic assumptions on the acceptance of results in the community.', 'Disconnect between theoretical computer science and empirical analysis.', 'Concept of small circuits for NP problems and their relation to polynomial time algorithms.', 'Existential question of whether the Hamiltonian circuit problem has a small circuit.', 'Hierarchy in complexity theory with P and NP as the first and second levels.', 'Potential collapse of the NP hierarchy if NP had small circuits.', 'Limited theoretical understanding in machine learning despite empirical success.', 'Successes and high demand in machine learning for image processing, robotics, and game playing.', 'Ethical questions and potential benefits of DNA editing in agriculture and medicine.', 'Challenges and potential benefits of genetic engineering and algorithms in biology.', 'Significance of analyzing genomic data for studying ancestry, disease tendencies, and personalized treatment.', 'Importance of preparation for effective teaching and flexibility in the classroom.', 'Individualized approach required for teaching to cater to diverse student needs.', "Karp's academic awakening through research and excelling in a mathematical methods course."]}