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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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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