Facility location: distributed approximation

In this paper, we initiate the study of the approximability of the facility location problem in a distributed setting. In particular, we explore a trade-off between the amount of communication and the resulting approximation ratio. We give a distributed algorithm that, for every constant k, achieves an O( √ k(mρ)1/ √ k log (m + n)) approximation in O(k) communication rounds where message size is bounded to O(log n) bits. The number of facilities and clients are m and n, respectively, and ρ is a coefficient that depends on the cost values of the instance. Our technique is based on a distributed primal-dual approach for approximating a linear program, that does not form a covering or packing program. Categories and Subject Descriptors F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems—computations on discrete structures; G.2.2 [Discrete Mathematics]: Graph Theory—graph algorithms; G.2.2 [Discrete Mathematics]: Graph Theory—network pr...

• Type: Conference
• Year: 2005
• Where: PODC
• Authors: Thomas Moscibroda, Roger Wattenhofer
• Keywords: Discrete Mathematics, Distributed And Parallel Computing, Facility Location, Facility Location Problem, PODC 2005