Improved Approximation Algorithms for the Partial Vertex Cover Problem

Authors:
Eran Halperin;Aravind Srinivasan
Affiliations:
-;-
Venue:
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Year:
2002

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Abstract

The partial vertex cover problemis a generalization of the vertex cover problem: given an undirected graph G = (V,E) and an integer k, we wish to choose a minimum number of vertices such that at least k edges are covered. Just as for vertex cover, 2-approximation algorithms are known for this problem, and it is of interest to see if we can do better than this. The current-best approximation ratio for partial vertex cover, when parameterized by the maximum degree d of G, is (2-驴(1/d)). We improve on this by presenting a (2-驴(ln ln d/ln d))-approximation algorithm for partial vertex cover using semidefinite programming, matching the current-best bound for vertex cover. Our algorithm uses a new rounding technique, which involves a delicate probabilistic analysis.