On the Parameterized Complexity of the Expected Coverage Problem

Abstract

The Maximum covering location problem (MCLP) is a well-studied problem in the field of operations research. Given a network with demands (demands can be positive or negative) on the nodes, an integer budget k, the MCLP seeks to find k potential facility centers in the network such that the neighborhood coverage is maximized. We study the variant of MCLP where edges of the network are subject to random failures due to some disruptive events. One of the popular models capturing the unreliable nature of the facility location is the linear reliable ordering (LRO) model. In this model, with every edge e of the network, we associate its survival probability \(0\le p_e\le 1\), or equivalently, its failure probability \(1-p_e\). The failure correlation in LRO is the following: If an edge e fails then every edge \(e'\) with \(p_{e'} \le p_e\) surely fails. The task is to identify the positions of k facilities that maximize the expected coverage. We refer to this problem as Expected Coverage problem. We study the Expected Coverage problem from the parameterized complexity perspective and obtain the following results.