lec21 - Introduction to Algorithms 6.046J/18.401 Lecture 21...

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Introduction to Algorithms 6.046J/18.401 Lecture 21 Prof. Piotr Indyk
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Introduction to Algorithms May 6, 2003 L20.2 © 2003 by Piotr Indyk P vs NP (interconnectedness of all things) A whole course by itself We’ll do just two lectures More in 6.045, 6.840J, etc.
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Introduction to Algorithms May 6, 2003 L20.3 © 2003 by Piotr Indyk Have seen so far Algorithms for various problems – Running times O(nm 2 ),O(n 2 ) ,O(n log n), O(n), etc. – I.e., polynomial in the input size Can we solve all (or most of) interesting problems in polynomial time ? Not really…
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Introduction to Algorithms May 6, 2003 L20.4 © 2003 by Piotr Indyk Example difficult problem Traveling Salesperson Problem (TSP) – Input: undirected graph with lengths on edges – Output: shortest tour that visits each vertex exactly once Best known algorithm: O(n 2 n ) time.
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Introduction to Algorithms May 6, 2003 L20.5 © 2003 by Piotr Indyk Another difficult problem Clique: – Input: undirected graph G=(V,E) – Output: largest subset C of V such that every pair of vertices in C has an edge between them Best known algorithm: O(n 2 n ) time
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Introduction to Algorithms May 6, 2003 L20.6
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lec21 - Introduction to Algorithms 6.046J/18.401 Lecture 21...

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