Abstract

We present improved combinatorial approximation algorithms for the uncapacitated facility location problem. Two central ideas in most of our results are cost scaling and greedy improvement. We present a simple greedy local search algorithm which achieves an approximation ratio of $2.414+\epsilon$ in $\tilde{O}(n^2/\epsilon)$ time. This also yields a bicriteria approximation tradeoff of $(1+\gamma,1+2/\gamma)$ for facility cost versus service cost which is better than previously known tradeoffs and close to the best possible. Combining greedy improvement and cost scaling with a recent primal-dual algorithm for facility location due to Jain and Vazirani, we get an approximation ratio of $1.853$ in $\tilde{O}(n^3)$ time. This is very close to the approximation guarantee of the best known algorithm which is linear programming (LP)-based. Further, combined with the best known LP-based algorithm for facility location, we get a very slight improvement in the approximation factor for facility location, achieving $1.728$. We also consider a variant of the capacitated facility location problem and present improved approximation algorithms for this.

MSC codes

  1. 68W25
  2. 90B80
  3. 90C27

MSC codes

  1. approximation algorithms
  2. facility location
  3. local search
  4. combinatorial optimization

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Published In

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 803 - 824
ISSN (online): 1095-7111

History

Published online: 27 July 2006

MSC codes

  1. 68W25
  2. 90B80
  3. 90C27

MSC codes

  1. approximation algorithms
  2. facility location
  3. local search
  4. combinatorial optimization

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