Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP

Authors:
Kamal Jain;Mohammad Mahdian;Evangelos Markakis;Amin Saberi;Vijay V. Vazirani
Affiliations:
Microsoft Research, Redmond, Washington;Laboratory for Computer Science, MIT, Cambridge, Massachusetts;Georgia Institute of Technology, Atlanta, Georgia;Georgia Institute of Technology, Atlanta, Georgia;Georgia Institute of Technology, Atlanta, Georgia
Venue:
Journal of the ACM (JACM)
Year:
2003

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Abstract

In this article, we will formalize the method of dual fitting and the idea of factor-revealing LP. This combination is used to design and analyze two greedy algorithms for the metric uncapacitated facility location problem. Their approximation factors are 1.861 and 1.61, with running times of O(m log m) and O(n3), respectively, where n is the total number of vertices and m is the number of edges in the underlying complete bipartite graph between cities and facilities. The algorithms are used to improve recent results for several variants of the problem.