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.
|Title of host publication||Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS|
|Publisher||IEEE Computer Society|
|Number of pages||10|
|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
|Name||Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS|
|Other||55th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2014|
|Period||14/10/18 → 14/10/21|
Bibliographical notePublisher Copyright:
© 2014 IEEE.
All Science Journal Classification (ASJC) codes
- Computer Science(all)