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note10 - Outline 1 2 3 4 5 6 7 8 9 10 11 12 NP-Completeness...

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Outline 1 NP-Completeness Theory 2 Limitation of Computation 3 Examples 4 Decision Problems 5 Verification Algorithm 6 Non-Deterministic Algorithm 7 NP-Complete Problems 8 Cook’s 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

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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 efficient algorithms for solving it. c Xin He (University at Buffalo) CSE 431/531 Algorithm Analysis and Design 2 / 110

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NP-Completeness Theory The topics we discussed so far are positive results: Given a problem, how to design efficient 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 efficient algorithms for solving it. NP-Completeness (NPC for sort) Theory is negative results . It studies the problems that cannot be solved efficiently . c Xin He (University at Buffalo) CSE 431/531 Algorithm Analysis and Design 2 / 110

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NP-Completeness Theory The topics we discussed so far are positive results: Given a problem, how to design efficient algorithms for solving it. NP-Completeness (NPC for sort) Theory is negative results . It studies the problems that cannot be solved efficiently . 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 efficient algorithms for solving it. NP-Completeness (NPC for sort) Theory is negative results . It studies the problems that cannot be solved efficiently . 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

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NP-Completeness Theory The topics we discussed so far are positive results: Given a problem, how to design efficient algorithms for solving it. NP-Completeness (NPC for sort) Theory is negative results . It studies the problems that cannot be solved efficiently . 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. 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 efficient algorithms for solving it.

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note10 - Outline 1 2 3 4 5 6 7 8 9 10 11 12 NP-Completeness...

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