Improved approximation algorithms for the partial vertex cover problem

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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−Θ(1/d)). We improve on this by presenting a (formula presented)-approximation algorithm for partial vertex cover using semidefinite programming, matching the current-best bound for vertex cover. Our algorithmuses a new rounding technique, which involves a delicate probabilistic analysis.

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Halperin, E., & Srinivasan, A. (2002). Improved approximation algorithms for the partial vertex cover problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2462, pp. 161–174). Springer Verlag. https://doi.org/10.1007/3-540-45753-4_15

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