Constant-Factor FPT Approximation for Capacitated k-Median

Authors Marek Adamczyk, Jarosław Byrka, Jan Marcinkowski , Syed M. Meesum, Michał Włodarczyk

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Marek Adamczyk
  • University of Warsaw, Poland
Jarosław Byrka
  • University of Wrocław, Poland
Jan Marcinkowski
  • University of Wrocław, Poland
Syed M. Meesum
  • University of Wrocław, Poland
Michał Włodarczyk
  • University of Warsaw, Poland

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Marek Adamczyk, Jarosław Byrka, Jan Marcinkowski, Syed M. Meesum, and Michał Włodarczyk. Constant-Factor FPT Approximation for Capacitated k-Median. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 1:1-1:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Facility location and clustering
  • Theory of computation → Fixed parameter tractability
  • K-median
  • Clustering
  • Approximation Algorithms
  • Fixed Parameter Tractability


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