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 (2007). Byrka proposed an algorithm parametrized by γ   and used it with γ≈1.6774γ≈1.6774. By either running his algorithm or the algorithm proposed by Jain, Mahdian and Saberi (STOCʼ02), Byrka obtained an algorithm that gives expected approximation ratio 1.5. We show that if γ is randomly selected, 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.