A 1.488 approximation algorithm for the uncapacitated facility location problem

We present a 1.488 approximation algorithm for the metric uncapacitated facility location (UFL) problem. Previously the best algorithm was due to Byrka [1]. By linearly combining two algorithms A1(γf) for γf ≈ 1.6774 and the (1.11, 1.78)-approximation algorithm A2 proposed by Jain, Mahdian and Saberi [8], Byrka gave a 1.5 approximation algorithm for the UFL problem. We show that if γf is randomly selected from some distribution, the approximation ratio can be improved to 1.488. Our algorithm cuts the gap with the 1.463 approximability lower bound by almost 1/3.

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