Abstract
The partial vertex cover problem is 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 \( \left( {2 - \Theta \left( {\tfrac{{\ln \ln d}} {{\ln d}}} \right)} \right) \) -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.
Supported in part by NSF grants CCR-9820951 and CCR-0121555 and DARPA cooperative agreement F30602-00-2-0601.
Supported in part by NSF Award CCR-0208005.
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Halperin, E., Srinivasan, A. (2002). Improved Approximation Algorithms for the Partial Vertex Cover Problem. In: Jansen, K., Leonardi, S., Vazirani, V. (eds) Approximation Algorithms for Combinatorial Optimization. APPROX 2002. Lecture Notes in Computer Science, vol 2462. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45753-4_15
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DOI: https://doi.org/10.1007/3-540-45753-4_15
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