08 - Spring 2010 CS530 Analysis of Algorithms Homework 8...

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Spring 2010 CS530 – Analysis of Algorithms Homework 8 H OMEWORK 8, DUE A PRIL 14 You must prove your answer to every question. Problems with a ( * ) in place of a score may be a little too advanced, or too challenging to most students, so I do not assign a score to them. But I will still note if you solve them. Problem 1. (10pts) In an undirected graph, a matching is a set of disjoint edges. Formulate precisely the four NP-related problems connected with the maximum matching problem: a decision problem, a search problem, maxi- mization problem and maximum-search problem. Solution. One common input of the problems is an undirected graph G = ( V , E ) given, for example, by its adjacency matrix showing which edge is adjacent to which vertex. For the decision problem, a number k is also given and it is asked whether G has a matching of size k (or larger). For the search problem, a number k is also given and in case there is a matching of size k we expect the solution to return one such matching. In the optimization problem, the desired output is the size of the largest
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08 - Spring 2010 CS530 Analysis of Algorithms Homework 8...

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