Abstract
We study the Capacitated k-Median problem, for which all the known constant factor approximation algorithms violate either the number of facilities or the capacities. While the standard LP-relaxation can only be used for algorithms violating one of the two by a factor of at least two, Li [10, 11] gave algorithms violating the number of facilities by a factor of \(1+\epsilon \) exploring properties of extended relaxations.
In this paper we develop a constant factor approximation algorithm for hard Uniform Capacitated k-Median violating only the capacities by a factor of \(1\,+\,\epsilon \). The algorithm is based on a configuration LP. Unlike in the algorithms violating the number of facilities, we cannot simply open extra few facilities at selected locations. Instead, our algorithm decides about the facility openings in a carefully designed dependent rounding process.
B. Rybicki—Research supported by NCN 2012/07/N/ST6/03068 grant.
S. Uniyal—Partially supported by the ERC StG project NEWNET No. 279352.
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Byrka, J., Rybicki, B., Uniyal, S. (2016). An Approximation Algorithm for Uniform Capacitated k-Median Problem with \(1+\epsilon \) Capacity Violation. In: Louveaux, Q., Skutella, M. (eds) Integer Programming and Combinatorial Optimization. IPCO 2016. Lecture Notes in Computer Science(), vol 9682. Springer, Cham. https://doi.org/10.1007/978-3-319-33461-5_22
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DOI: https://doi.org/10.1007/978-3-319-33461-5_22
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