A Better Approximation Ratio and an IP Formulation for a Sensor Cover Problem

Abstract

We study a one-dimensional sensor cover problem, known as the Restricted Strip Cover (RSC) problem, defined as follows. We are given an interval U of the real line, and a set of n sensors, each of which covers some subinterval of U and is powered with a battery of limited duration. The RSC problem consists in assigning a starting time to each sensor so that the whole interval U is covered for as long as possible. We assume that when a sensor is turned on (at its starting time) it remains on through the duration of its battery.

Buchsbaum, Efrat, Jain, Venkatasubramanian and Yi showed that RSC is NP-hard and designed an O(loglogn)-approximation algorithm. More recently, Gibson and Varadarajan presented a greedy-like algorithm which they proved to have approximation ratio at most 5. We prove that the approximation ratio of this algorithm is 4, and exhibit an instance showing that this ratio is tight. We also show an integer programming formulation for this problem and present some computational results obtained with the implementation of this approach. For the same set of instances, we compute the quality of the solution found by the approximation algorithm.