lec22 - Introduction to Algorithms 6.046J/18.401 Lecture 22...

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Introduction to Algorithms 6.046J/18.401 Lecture 22 Prof. Piotr Indyk
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Introduction to Algorithms May 8, 2003 L20.2 © 2003 by Piotr Indyk P vs NP (Episode II) We defined a large class of interesting problems, namely NP – Decision problems (YES or NO) – Solvable in non-deterministic polynomial time. I.e., a solution can be verified in polynomial time We have a way of saying that one problem is not harder than another ( ) Our goal: show equivalence between hard problems
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Introduction to Algorithms May 8, 2003 L20.3 © 2003 by Piotr Indyk Reductions: ’ to A for YES NO f x’ f(x’)= A’ for x YES NO
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Introduction to Algorithms May 8, 2003 L20.4 © 2003 by Piotr Indyk Showing equivalence between difficult problems TSP P3 P4 Clique P5 Options: – Show reductions between all pairs of problems – Reduce the number of reductions (!) using transitivity of “ – Show that all problems in NP a reducible to a fixed . To show that some problem NP is equivalent to all difficult problems, we only show ’.
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Introduction to Algorithms May 8, 2003 L20.5 © 2003 by Piotr Indyk The first problem Satisfiability problem (SAT): – Given: a formula
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This note was uploaded on 10/08/2009 for the course EECS 6.046 taught by Professor Erikdemaine during the Spring '04 term at MIT.

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lec22 - Introduction to Algorithms 6.046J/18.401 Lecture 22...

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