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 language | English |
|---|---|
| Title of host publication | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
| Publisher | IEEE Computer Society |
| Pages | 256-265 |
| Number of pages | 10 |
| ISBN (Electronic) | 9781479965175 |
| DOIs | |
| Publication status | Published - 2014 Dec 7 |
| Event | 55th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2014 - Philadelphia, United States Duration: 2014 Oct 18 → 2014 Oct 21 |
Publication series
| Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
|---|---|
| ISSN (Print) | 0272-5428 |
Other
| Other | 55th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2014 |
|---|---|
| Country | United States |
| City | Philadelphia |
| Period | 14/10/18 → 14/10/21 |
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All Science Journal Classification (ASJC) codes
- Computer Science(all)
Cite this
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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 proceeding › Conference 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.
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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 -