CC2203-Les16NP-Complete-for-viewing

CC2203-Les16NP-Complete-for-viewing - Lesson 16: P, NP,...

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Unformatted text preview: Lesson 16: P, NP, NP-Completeness Computational Complexity Problem Concern about whether a problem can be solved in polynomial time by some algorithm 16-1/9 16-2/9 Classifying a problem’s complexity Is there a polynomial-time algorithm that solves the problem? Possible answers: l yes l no • because it can be proved that all algorithms take exponential time • because it can be proved that no algorithm exists at all to solve this problem l don’t know l don’t know, but if such algorithm were to be found, then it would provide a means of solving many other problems in polynomial time 16-3/9 Types of problems l Optimization problem: construct a solution that maximizes or minimizes some objective function l Decision problem: answer yes/no to a question Many problems will have decision and optimization versions. 16-4/9 The class P P : the class of decision problems that are solvable in O ( p ( n )), where p ( n ) is a polynomial on n Why polynomial?...
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This note was uploaded on 08/18/2011 for the course COMP 3868 taught by Professor Keithchan during the Summer '97 term at Hong Kong Polytechnic University.

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CC2203-Les16NP-Complete-for-viewing - Lesson 16: P, NP,...

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