Episode
#111 – Richard Karp: Algorithms and Computational Complexity
2:07:59
Published: Sun Jul 26 2020
Description
Richard Karp is a professor at Berkeley and one of the most important 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. Support this podcast by supporting our sponsors: - Eight Sleep: https://eightsleep.com/lex - Cash App – use code "LexPodcast" and download: - Cash App (App Store): https://apple.co/2sPrUHe - Cash App (Google Play): https://bit.ly/2MlvP5w If you would like to get more information about this podcast go to https://lexfridman.com/ai or connect with @lexfridman on Twitter, LinkedIn, Facebook, Medium, or YouTube where you can watch the video versions of these conversations. If you enjoy the podcast, please rate it 5 stars on Apple Podcasts, follow on Spotify, or support it on Patreon. Here's the outline of the episode. On some podcast players you should be able to click the timestamp to jump to that time. OUTLINE: 00:00 - Introduction 03:50 - Geometry 09:46 - 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
Chapters
In this podcast, Lex Fridman interviews Robert Tarjan, a computer scientist who received the Turing Award in 1985 for his work in algorithm theory, including the development of the Adman's Karp algorithm and Hopcroft Karp algorithm.
00:00 - 03:45 (03:45)
Summary
In this podcast, Lex Fridman interviews Robert Tarjan, a computer scientist who received the Turing Award in 1985 for his work in algorithm theory, including the development of the Adman's Karp algorithm and Hopcroft Karp algorithm.
Episode#111 – Richard Karp: Algorithms and Computational Complexity
PodcastLex Fridman Podcast
Michael Rabin shares a story about a problem he encountered as a young student - finding the shortest distance between two non-overlapping circles - and the solution he discovered.
03:45 - 18:49 (15:03)
Summary
Michael Rabin shares a story about a problem he encountered as a young student - finding the shortest distance between two non-overlapping circles - and the solution he discovered. It turns out that the straight line between the two centers of the circles provides the shortest distance, as any other line connecting the circles would be on a longer path.
Episode#111 – Richard Karp: Algorithms and Computational Complexity
PodcastLex Fridman Podcast
The speaker reflects on his past amusement of mental math and noticing the significant technological advancements since then, including the multitude of computers in the world and their ability to solve complex problems.
18:49 - 25:10 (06:21)
Summary
The speaker reflects on his past amusement of mental math and noticing the significant technological advancements since then, including the multitude of computers in the world and their ability to solve complex problems.
Episode#111 – Richard Karp: Algorithms and Computational Complexity
PodcastLex Fridman Podcast
The question of whether it's possible to achieve human-level intelligence through artificial intelligence (AI) is still up for debate.
25:10 - 30:21 (05:11)
Summary
The question of whether it's possible to achieve human-level intelligence through artificial intelligence (AI) is still up for debate. While some argue that the human brain is just a set of interconnected switches, others point to the emotional complexity of human intelligence as an obstacle to creating algorithms that fully replicate it.
Episode#111 – Richard Karp: Algorithms and Computational Complexity
PodcastLex Fridman Podcast
The exponential improvement of technology makes it difficult to gauge the potential for artificial intelligence.
30:21 - 39:59 (09:37)
Summary
The exponential improvement of technology makes it difficult to gauge the potential for artificial intelligence. Though there is potential for machines to perform certain tasks, ways to improve intelligence itself may prove much harder to achieve.
Episode#111 – Richard Karp: Algorithms and Computational Complexity
PodcastLex Fridman Podcast
This podcast episode explains the concept of polynomial time algorithms as ones whose running time is proportional to a fixed power of the size of the input, allowing for more efficient problem solving in real-world systems.
39:59 - 47:34 (07:34)
Summary
This podcast episode explains the concept of polynomial time algorithms as ones whose running time is proportional to a fixed power of the size of the input, allowing for more efficient problem solving in real-world systems.
Episode#111 – Richard Karp: Algorithms and Computational Complexity
PodcastLex Fridman Podcast
In this episode, the host explains how the satisfiability problem of propositional logic is a universal combinatorial problem and describes Stephen Cook's contribution to complexity theory.
47:34 - 1:02:10 (14:36)
Summary
In this episode, the host explains how the satisfiability problem of propositional logic is a universal combinatorial problem and describes Stephen Cook's contribution to complexity theory. The episode also discusses the difficulty of finding cliques.
Episode#111 – Richard Karp: Algorithms and Computational Complexity
PodcastLex Fridman Podcast
This episode discusses how the satisfiability problem can be converted into the independent set problem and how the propositional logic problem can be rewritten using operations of Boolean logic.
1:02:10 - 1:13:17 (11:07)
Summary
This episode discusses how the satisfiability problem can be converted into the independent set problem and how the propositional logic problem can be rewritten using operations of Boolean logic. It also explores how various commonly occurring problems in NP have the same expressive power as the satisfiability problem.
Episode#111 – Richard Karp: Algorithms and Computational Complexity
PodcastLex Fridman Podcast
This episode discusses the stable matching problem and various algorithms used to solve it, such as the Hopcroft Karp algorithm for finding maximum cardinality matchings in bipartite graphs.
1:13:17 - 1:22:00 (08:42)
Summary
This episode discusses the stable matching problem and various algorithms used to solve it, such as the Hopcroft Karp algorithm for finding maximum cardinality matchings in bipartite graphs.
Episode#111 – Richard Karp: Algorithms and Computational Complexity
PodcastLex Fridman Podcast
The use of prime numbers in cryptography is explained through Fermat's Little theorem, which states that raising any number a in the range 0 through n-1 to the n-1th power, modulo n gives back the number a, if a is prime.
1:22:01 - 1:30:13 (08:12)
Summary
The use of prime numbers in cryptography is explained through Fermat's Little theorem, which states that raising any number a in the range 0 through n-1 to the n-1th power, modulo n gives back the number a, if a is prime.
Episode#111 – Richard Karp: Algorithms and Computational Complexity
PodcastLex Fridman Podcast
This podcast discusses the importance of analyzing the worst-case scenario in algorithms, especially analyzing average case probabilistic.
1:30:14 - 1:40:28 (10:14)
Summary
This podcast discusses the importance of analyzing the worst-case scenario in algorithms, especially analyzing average case probabilistic. The problem of cities, pairwise distances between cities, and finding a tour through all the cities that minimizes the total cost of all the edges traversed is also discussed.
Episode#111 – Richard Karp: Algorithms and Computational Complexity
PodcastLex Fridman Podcast
In this podcast, the guest discusses theoretical computer science and its relationship with analyzing real-world data.
1:40:29 - 1:46:12 (05:43)
Summary
In this podcast, the guest discusses theoretical computer science and its relationship with analyzing real-world data. They also explore the most compelling open problems and potential breakthroughs in the field.
Episode#111 – Richard Karp: Algorithms and Computational Complexity
PodcastLex Fridman Podcast
The hosts discuss the relationship between theoretical computer science and machine learning, touching on the topics of small circuits for specific problems and the history and progression of the machine learning field.
1:46:13 - 1:54:36 (08:23)
Summary
The hosts discuss the relationship between theoretical computer science and machine learning, touching on the topics of small circuits for specific problems and the history and progression of the machine learning field.
Episode#111 – Richard Karp: Algorithms and Computational Complexity
PodcastLex Fridman Podcast
The human brain is a complex structure that can be studied by analyzing genomic data to determine how genes operate and how proteins interact with each other.
1:54:37 - 2:01:39 (07:02)
Summary
The human brain is a complex structure that can be studied by analyzing genomic data to determine how genes operate and how proteins interact with each other. However, it is still unclear how the circuit of the brain provides us with simple characteristics like the edges of objects.
Episode#111 – Richard Karp: Algorithms and Computational Complexity
PodcastLex Fridman Podcast
A computer science professor shares his teaching strategies and reveals some of the big "aha" moments his students have had when learning about algorithms and computer science.
2:01:40 - 2:06:13 (04:33)
Summary
A computer science professor shares his teaching strategies and reveals some of the big "aha" moments his students have had when learning about algorithms and computer science.
Episode#111 – Richard Karp: Algorithms and Computational Complexity
PodcastLex Fridman Podcast
Richard Karp talks about his journey into theoretical computer science, his contributions to the field, and the significance of his P versus NP paper.
2:06:13 - 2:07:36 (01:22)
Summary
Richard Karp talks about his journey into theoretical computer science, his contributions to the field, and the significance of his P versus NP paper. No product advertisements found.