Improved LP-Rounding Approximation Algorithm for k-level Uncapacitated Facility Location
We study the k-level uncapacitated facility location problem, where clients need to be connected with paths crossing open facilities of k types (levels). In this paper we give an approximation algorithm that for any constant k, in polynomial time, delivers solutions of cost at most α k times OPT, where α k is an increasing function of k, with lim k → ∞ α k = 3.
Our algorithm rounds a fractional solution to an extended LP formulation of the problem. The rounding builds upon the technique of iteratively rounding fractional solutions on trees (Garg, Konjevod, and Ravi SODA’98) originally used for the group Steiner tree problem.
We improve the approximation ratio for k-UFL for all k ≥ 3, in particular we obtain the ratio equal 2.02, 2.14, and 2.24 for k = 3,4, and 5.
KeywordsApproximation Algorithm Cluster Center Facility Location Approximation Ratio Facility Location Problem
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