2026-07-25T10:03:40Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:11122 2024-03-06T10:47:29Z ddc:004 open_access

Constant-Factor FPT Approximation for Capacitated k-Median Adamczyk, Marek Byrka, Jarosław Marcinkowski, Jan Meesum, Syed M. Włodarczyk, Michał K-median Clustering Approximation Algorithms Fixed Parameter Tractability Capacitated k-median is one of the few outstanding optimization problems for which the existence of a polynomial time constant factor approximation algorithm remains an open problem. In a series of recent papers algorithms producing solutions violating either the number of facilities or the capacity by a multiplicative factor were obtained. However, to produce solutions without violations appears to be hard and potentially requires different algorithmic techniques. Notably, if parameterized by the number of facilities k, the problem is also W[2] hard, making the existence of an exact FPT algorithm unlikely. In this work we provide an FPT-time constant factor approximation algorithm preserving both cardinality and capacity of the facilities. The algorithm runs in time 2^O(k log k) n^O(1) and achieves an approximation ratio of 7+epsilon. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Marek Adamczyk and Jarosław Byrka and Jan Marcinkowski and Syed M. Meesum and Michał Włodarczyk 2019 Is Part Of LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2019.1 urn:nbn:de:0030-drops-111225 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.1 eng https://creativecommons.org/licenses/by/3.0/legalcode