Improved LP-Rounding Approximation Algorithm for k-level Uncapacitated Facility Location

  • Jaroslaw Byrka
  • Bartosz Rybicki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7391)


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.


Approximation Algorithm Cluster Center Facility Location Approximation Ratio Facility Location Problem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jaroslaw Byrka
    • 1
  • Bartosz Rybicki
    • 1
  1. 1.Institute of Computer ScienceUniversity of WroclawWrocławPoland

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