Improved Combinatorial Algorithms for the Facility Location and k-Median Problems

  • Authors:
  • Moses Charikar;Sudipto Guha

  • Affiliations:
  • -;-

  • Venue:
  • FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
  • Year:
  • 1999

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Abstract

We present improved combinatorial approximation algorithms for the uncapacitated facility location and k-median problems. 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 \math in \math time. This also yields a bicriteria approximation tradeoff of \math 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 \math time. This is already very close to the approximation guarantee of the best known algorithm which is 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 present improved approximation algorithms for capacitated facility location and a variant.We also present a 4-approximation for the k-median problem, using similar ideas, building on the 6-approximation of Jain and Vazirani. The algorithm runs in \math time.