Improved Combinatorial Algorithms for Facility Location Problems

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+ in Õ(n/ ) time. This also yields a bicriteria approximation tradeoff of (1 + γ, 1 + 2/γ) 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 Õ(n) time. This is 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 also consider a variant of the capacitated facility location problem and present improved approximation algorithms for this. ∗This work was done while while both authors were at Stanford University, Stanford, CA 94305, and their research was supported by he Pierre and Christine Lamond Fellowship, and the IBM Cooperative Fellowship, respectively, along with NSF Grant IIS-9811904 and NSF Award CCR-9357849, with matching funds from IBM, Mitsubishi, Schlumberger Foundation, Shell Foundation, and Xerox Corporation. †Department of Computer Science, Princeton University, 35 Olden Street, Princeton, NJ 08544. Email: [email protected] ‡Department of Computer Information Sciences, University of Pennsylvania, 3330 Walnut Street, Philadelphia, PA 19104. Email: [email protected]