note10 - Outline 1 NP-Completeness Theory 2 Limitation of...

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Unformatted text preview: Outline 1 NP-Completeness Theory 2 Limitation of Computation 3 Examples 4 Decision Problems 5 Verication Algorithm 6 Non-Deterministic Algorithm 7 NP-Complete Problems 8 Cooks Theorem 9 Turing Machine 10 Church-Turing Thesis 11 How to prove a problem is NP-complete? 12 Examples of NPC Proofs c Xin He (University at Buffalo) CSE 431/531 Algorithm Analysis and Design 1 / 110 NP-Completeness Theory The topics we discussed so far are positive results: c Xin He (University at Buffalo) CSE 431/531 Algorithm Analysis and Design 2 / 110 NP-Completeness Theory The topics we discussed so far are positive results: Given a problem, how to design efcient algorithms for solving it. c Xin He (University at Buffalo) CSE 431/531 Algorithm Analysis and Design 2 / 110 NP-Completeness Theory The topics we discussed so far are positive results: Given a problem, how to design efcient algorithms for solving it. NP-Completeness (NPC for sort) Theory is negative results . c Xin He (University at Buffalo) CSE 431/531 Algorithm Analysis and Design 2 / 110 NP-Completeness Theory The topics we discussed so far are positive results: Given a problem, how to design efcient algorithms for solving it. NP-Completeness (NPC for sort) Theory is negative results . It studies the problems that cannot be solved efciently . c Xin He (University at Buffalo) CSE 431/531 Algorithm Analysis and Design 2 / 110 NP-Completeness Theory The topics we discussed so far are positive results: Given a problem, how to design efcient algorithms for solving it. NP-Completeness (NPC for sort) Theory is negative results . It studies the problems that cannot be solved efciently . Why we study negative results? c Xin He (University at Buffalo) CSE 431/531 Algorithm Analysis and Design 2 / 110 NP-Completeness Theory The topics we discussed so far are positive results: Given a problem, how to design efcient algorithms for solving it. NP-Completeness (NPC for sort) Theory is negative results . It studies the problems that cannot be solved efciently . Why we study negative results? In some sense, the negative results are more important than positive results: c Xin He (University at Buffalo) CSE 431/531 Algorithm Analysis and Design 2 / 110 NP-Completeness Theory The topics we discussed so far are positive results: Given a problem, how to design efcient algorithms for solving it. NP-Completeness (NPC for sort) Theory is negative results . It studies the problems that cannot be solved efciently . Why we study negative results? In some sense, the negative results are more important than positive results: The negative result may say that a given problem Q cannot be solved in polynomial time....
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This note was uploaded on 02/27/2012 for the course CSE 431/531 taught by Professor Xinhe during the Fall '11 term at SUNY Buffalo.

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note10 - Outline 1 NP-Completeness Theory 2 Limitation of...

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