# Algorithm Design and Analysis

May 5th, 2015
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Easy problems - class P Decision problems vs. Optimization problems Class NP Reductions NP-complete class

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Algorithm Design and AnalysisAlgorithm Analysis and Design NP-CompletenessPham Quang DungHanoi, 2012Pham Quang Dung ()Algorithm Analysis and Design NP-CompletenessHanoi, 20121 / 31Outline1Easy problems - class P Decision problems vs. Optimization problems Class NP Reductions NP-complete class2345Pham Quang Dung ()Algorithm Analysis and Design NP-CompletenessHanoi, 20122 / 31Class P: Problems that are solvable by polynomial-time algorithms (O(nk ) where n is the size of the input to the problem and k is some constant) Examples: Sorting Shortest path problems Minimum Spanning Tree problems Maximum Flow problems ...Pham Quang Dung ()Algorithm Analysis and Design NP-CompletenessHanoi, 20123 / 31Outline1Easy problems - class P Decision problems vs. Optimization problems Class NP Reductions NP-complete class2345Pham Quang Dung ()Algorithm Analysis and Design NP-CompletenessHanoi, 20124 / 31Decision problemsAnswer is yes or noIs n a prime number? Does an undirected graph contain a hamilton cycle? Satisability: Given a boolean formula. Does there exist some assignment of the values 0 and 1 to its variables such that the value of the formula is 1? Subset sum problem: Given a set of integers S = {x1 , . . . , xn } and an integer T . Is there a subset of S whose sum is equal to T ?Pham Quang Dung ()Algorithm Analysis and Design NP-CompletenessHanoi, 20125 / 31Optimization problemsEa

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