paper

A Constant Factor Approximation Algorithm for Fault-Tolerant k-Median

arXiv:1307.2808 · doi:10.1137/1.9781611973402.1

Abstract

In this paper, we consider the fault-tolerant $k$ -median problem and give the \emph{first} constant factor approximation algorithm for it. In the fault-tolerant generalization of classical $k$ -median problem, each client $j$ needs to be assigned to at least $r_{j} \geq 1$ distinct open facilities. The service cost of $j$ is the sum of its distances to the $r_{j}$ facilities, and the $k$ -median constraint restricts the number of open facilities to at most $k$ . Previously, a constant factor was known only for the special case when all $r_{j}$ s are the same, and a logarithmic approximation ratio for the general case. In addition, we present the first polynomial time algorithm for the fault-tolerant $k$ -median problem on a path or a HST by showing that the corresponding LP always has an integral optimal solution. We also consider the fault-tolerant facility location problem, where the service cost of $j$ can be a weighted sum of its distance to the $r_{j}$ facilities. We give a simple constant factor approximation algorithm, generalizing several previous results which only work for nonincreasing weight vectors.

19 pages