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Unformatted text preview: Lesson 16: P, NP, NPCompleteness Computational Complexity Problem Concern about whether a problem can be solved in polynomial time by some algorithm 161/9 162/9 Classifying a problem’s complexity Is there a polynomialtime 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 163/9 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. 164/9 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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 Summer '97
 KEITHCHAN
 Computational complexity theory, polynomial time, Nondeterministic Polynomialtime

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