Algorithms Column:The Vertex Cover Problem Samir Khuller Department of Computer Science University of Maryland, College Park, MD 20742 samir@cs, umd. edu Copyright (~) Samir Khuller, 2002 In this column I give a slightly simpler proof of an old result by Nemhauser and Trotter [10]. It would be interesting to see for which other problems such results hold. One of the widely studied problems in Combinatorial Optimization is the Weighted Vertex Cover problem. Given a graph G = (V, E) with a weight function defined on the vertices, a vertex cover is a subset of vertices S such that for each edge e = (u, v) either u E S or v 6 S. The m i n i m u m weight vertex cover problem asks for a vertex cover of minimum total weight. This problem has been the subject of many papers, since the problem is N P - h a r d , but can be solved optimally for bipartite graphs by a reduction to network flows. There are many papers addressing the issue of obtaining polynomial time approximation algorithms [1, 2, 3, 4, 5, 8, 7]. One of the first approaches (in fact this also
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Algorithms column: the vertex cover problem
Khuller, Samir
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, Volume 33 (2)
Association for Computing Machinery – Jun 1, 2002
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