LP-based algorithms for capacitated facility location

Hyung-Chan An, Mohit Singh, Ola Svensson

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

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
Volume46
Issue number1
DOIs
Publication statusPublished - 2017 Jan 1

Fingerprint

Facility Location
Linear programming
Linear Programming Relaxation
Facility Location Problem
Integrality
Rounding
Approximation Algorithms
Approximation algorithms
Primal-dual Method
Multicommodity Flow
Performance Guarantee
Methodology
Combinatorial Optimization Problem
Local Search
Combinatorial optimization
Demonstrate

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Mathematics(all)

Cite this

An, Hyung-Chan ; Singh, Mohit ; Svensson, Ola. / LP-based algorithms for capacitated facility location. In: SIAM Journal on Computing. 2017 ; Vol. 46, No. 1. pp. 272-306.
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LP-based algorithms for capacitated facility location. / An, Hyung-Chan; Singh, Mohit; Svensson, Ola.

In: SIAM Journal on Computing, Vol. 46, No. 1, 01.01.2017, p. 272-306.

Research output: Contribution to journalArticle

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