LP-based algorithms for capacitated facility location

Hyung Chan An, Mohit Singh, Ola Svensson

Research output: Contribution to journalArticlepeer-review

37 Citations (Scopus)


Linear programming (LP) has played a key role in the study of algorithms for combinatorial optimization problems. In the field of approximation algorithms, this is well illustrated by the uncapacitated facility location problem. A variety of algorithmic methodologies, such as LP-rounding and the primal-dual method, have been applied to and evolved from algorithms for this problem. Unfortunately, this collection of powerful algorithmic techniques had not yet been applicable to the more general capacitated facility location problem. In fact, all of the known algorithms with good performance guarantees were based on a single technique, local search, and no LP relaxation was known to efficiently approximate the problem. In this paper, we present an LP relaxation with a constant integrality gap for the capacitated facility location. We demonstrate that the fundamental theories of multicommodity flows and matchings provide key insights that lead to the strong relaxation. Our algorithmic proof of integrality gap is obtained by finally accessing the rich toolbox of LP-based methodologies: we present a constant factor approximation algorithm based on LP-rounding.

Original languageEnglish
Pages (from-to)272-306
Number of pages35
JournalSIAM Journal on Computing
Issue number1
Publication statusPublished - 2017

Bibliographical note

Publisher Copyright:
© 2017 Society for Industrial and Applied Mathematics.

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Mathematics(all)


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