@inproceedings{a9e7b2b7668d47f7a49a9939c7b2ae01,

title = "Constant-factor FPT approximation for capacitated k-median",

abstract = "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 2O(k log k)nO(1) and achieves an approximation ratio of 7 + ε.",

keywords = "Approximation algorithms, Clustering, Fixed parameter tractability, K-median",

author = "Marek Adamczyk and Jaros{\l}aw Byrka and Jan Marcinkowski and Meesum, {Syed M.} and Micha{\l} W{\l}odarczyk",

note = "Funding Information: Funding Jaros{\l}aw Byrka: Supported by the Polish National Science Centre grant 2015/18/E/ST6/ 00456. Jan Marcinkowski: Supported by the Polish National Science Centre grant 2015/18/E/ST6/00456. Syed M. Meesum: Supported by the Polish National Science Centre grant 2015/18/E/ST6/00456. Publisher Copyright: {\textcopyright} Marek Adamczyk, Jaros{\l}aw Byrka, Jan Marcinkowski, Syed M. Meesum, and Micha{\l} W{\l}odarczyk.; 27th Annual European Symposium on Algorithms, ESA 2019 ; Conference date: 09-09-2019 Through 11-09-2019",

year = "2019",

month = sep,

day = "1",

doi = "10.4230/LIPIcs.ESA.2019.1",

language = "English",

series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

editor = "Bender, {Michael A.} and Ola Svensson and Grzegorz Herman",

booktitle = "27th Annual European Symposium on Algorithms, ESA 2019",

address = "Germany",

}