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arXiv · 1307.2808

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

Mohammadtaghi Hajiaghayi·Wei Hu·Jian Li·Shi Li·Barna Saha
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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 $r_j \ge 1$ 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.

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Mohammadtaghi Hajiaghayi, Wei Hu, Jian Li, Shi Li, Barna Saha. 2013-07-10. A Constant Factor Approximation Algorithm for Fault-Tolerant k-Median. https://doi.org/10.1137/1.9781611973402.1

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