Constant approximation for fault-tolerant median problems via iterative rounding

TL;DR

This paper introduces a versatile iterative rounding framework that achieves a constant-factor approximation for fault-tolerant median problems, encompassing various clustering and facility location challenges.

Contribution

The paper presents a novel iterative rounding approach that unifies and improves approximation guarantees for multiple fault-tolerant median problems.

Findings

Achieves a constant-factor approximation for fault-tolerant median problems.

Unifies several clustering and facility location problems under a single framework.

Provides a versatile method applicable to various fault-tolerant optimization problems.

Abstract

In this paper, we study the fault-tolerant matroid median and fault-tolerant knapsack median problems. These two problems generalize many fundamental clustering and facility location problems, such as uniform fault-tolerant $k$-median, uniform fault-tolerant facility location, matroid median, knapsack median, etc. We present a versatile iterative rounding framework and obtain a unifying constant-factor approximation algorithm.