LP-based algorithms for capacitated facility location

Hyung Chan An, Mohit Singh, Ola Svensson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

28 Citations (Scopus)

Abstract

Linear programming 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 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 linear programming relaxation was known to efficiently approximate the problem. In this paper, we present a linear programming relaxation with constant integrality gap for capacitated facility location. We demonstrate that the fundamental theories of multi-commodity 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
Title of host publicationProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
PublisherIEEE Computer Society
Pages256-265
Number of pages10
ISBN (Electronic)9781479965175
DOIs
Publication statusPublished - 2014 Dec 7
Event55th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2014 - Philadelphia, United States
Duration: 2014 Oct 182014 Oct 21

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Other

Other55th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2014
CountryUnited States
CityPhiladelphia
Period14/10/1814/10/21

Fingerprint

Linear programming
Approximation algorithms
Combinatorial optimization
Local search (optimization)

All Science Journal Classification (ASJC) codes

  • Computer Science(all)

Cite this

An, H. C., Singh, M., & Svensson, O. (2014). LP-based algorithms for capacitated facility location. In Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS (pp. 256-265). [6979010] (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS). IEEE Computer Society. https://doi.org/10.1109/FOCS.2014.35
An, Hyung Chan ; Singh, Mohit ; Svensson, Ola. / LP-based algorithms for capacitated facility location. Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS. IEEE Computer Society, 2014. pp. 256-265 (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS).
@inproceedings{2c6990b5ff8b4dbbbe1309c1b46b511c,
title = "LP-based algorithms for capacitated facility location",
abstract = "Linear programming 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 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 linear programming relaxation was known to efficiently approximate the problem. In this paper, we present a linear programming relaxation with constant integrality gap for capacitated facility location. We demonstrate that the fundamental theories of multi-commodity 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.",
author = "An, {Hyung Chan} and Mohit Singh and Ola Svensson",
year = "2014",
month = "12",
day = "7",
doi = "10.1109/FOCS.2014.35",
language = "English",
series = "Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS",
publisher = "IEEE Computer Society",
pages = "256--265",
booktitle = "Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS",
address = "United States",

}

An, HC, Singh, M & Svensson, O 2014, LP-based algorithms for capacitated facility location. in Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS., 6979010, Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, IEEE Computer Society, pp. 256-265, 55th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2014, Philadelphia, United States, 14/10/18. https://doi.org/10.1109/FOCS.2014.35

LP-based algorithms for capacitated facility location. / An, Hyung Chan; Singh, Mohit; Svensson, Ola.

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS. IEEE Computer Society, 2014. p. 256-265 6979010 (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - LP-based algorithms for capacitated facility location

AU - An, Hyung Chan

AU - Singh, Mohit

AU - Svensson, Ola

PY - 2014/12/7

Y1 - 2014/12/7

N2 - Linear programming 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 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 linear programming relaxation was known to efficiently approximate the problem. In this paper, we present a linear programming relaxation with constant integrality gap for capacitated facility location. We demonstrate that the fundamental theories of multi-commodity 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.

AB - Linear programming 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 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 linear programming relaxation was known to efficiently approximate the problem. In this paper, we present a linear programming relaxation with constant integrality gap for capacitated facility location. We demonstrate that the fundamental theories of multi-commodity 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.

UR - http://www.scopus.com/inward/record.url?scp=84920008424&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84920008424&partnerID=8YFLogxK

U2 - 10.1109/FOCS.2014.35

DO - 10.1109/FOCS.2014.35

M3 - Conference contribution

AN - SCOPUS:84920008424

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 256

EP - 265

BT - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

PB - IEEE Computer Society

ER -

An HC, Singh M, Svensson O. LP-based algorithms for capacitated facility location. In Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS. IEEE Computer Society. 2014. p. 256-265. 6979010. (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS). https://doi.org/10.1109/FOCS.2014.35