Facility location with Service Installation Costs

  • Authors:

  • David B. Shmoys;Chaitanya Swamy;Retsef Levi

  • Affiliations:

  • Cornell University, Ithaca, NY;Cornell University, Ithaca, NY;Cornell University, Ithaca, NY

  • Venue:
  • SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
  • Year:
  • 2004

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Abstract

We consider a generalization of the uncapacitated facility location problem which we call Facility Location with Service Installation Costs. We are given a set of facilities, F,a set of demands or clients D, and a set of services S. Each facility i has a facility opening cost fi, and we have a service installation cost of fli for every facility-service pair (i, l). Each client j in D requests a specific service g(j) ∈ S and the cost of assigning a client j to facility i is given by cij. We want to open a set of facilities, install services at the open facilities, and assign each client j to an open facility at which service g(j) is installed, so as to minimize the sum of the facility opening costs, the service installation costs and the client assignment costs.Our main result is a primal-dual 6-approximation algorithm under the assumption that there is an ordering on the facilities such that if i comes before i' in this ordering then for every service type l, fli ≤ fl i. This includes (as special cases) the settings where the service installation cost fli depends only on the service type l, or depends only on the location i. With arbitrary service installation costs, the problem becomes as hard as the set-cover problem. Our algorithm extends the algorithm of Jain & Vazirani [9] in a novel way. If the service installation cost depends only on the service type and not on the location, we give an LP rounding algorithm that attains an improved approximation ratio of 2.391. The algorithm combines both clustered randomized rounding [6] and the filtering based technique of [10, 14]. We also consider the k-median version of the problem where there is an additional requirement that at most k facilities may be opened. We use our primal-dual algorithm to give a constant-factor approximation for this problem when the service installation cost depends only on the service type.