Abstract
In this paper we study the capacitated vertex cover problem, a generalization of the well-known vertex cover problem. Given a graph G = (V, E), the goal is to cover all the edges by picking a minimum cover using the vertices. When we pick a vertex, we can cover up to a pre-specified number of edges incident on this vertex (its capacity). The problem is clearly NP-hard as it generalizes the well-known vertex cover problem. Previously, 2-approximation algorithms were developed with the assumption that multiple copies of a vertex may be chosen in the cover. If we are allowed to pick at most a given number of copies of each vertex, then the problem is significantly harder to solve. Chuzhoy and Naor (Proc. IEEE Symposium on Foundations of Computer Science, 481–489, 2002) have recently shown that the weighted version of this problem is at least as hard as set cover; they have also developed a 3-approximation algorithm for the unweighted version. We give a 2-approximation algorithm for the unweighted version, improving the Chuzhoy-Naor bound of 3 and matching (up to lower-order terms) the best approximation ratio known for the vertex cover problem.
Research supported by NSF Award CCR-9820965.
Supported in part by NSF grants CCR-9820951 and CCR-0121555 and DARPA cooperative agreement F30602-00-2-0601.
Research supported by NSF Award CCR-9820965 and an NSF CAREER Award CCR-9501355.
Supported in part by NSF Award CCR-0208005.
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Gandhi, R., Halperin, E., Khuller, S., Kortsarz, G., Srinivasan, A. (2003). An Improved Approximation Algorithm for Vertex Cover with Hard Capacities. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_15
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DOI: https://doi.org/10.1007/3-540-45061-0_15
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