Finding the Quality of Line Coverage of a Sensor Network

Abstract

The coverage problem in wireless sensor networks addresses the problem of covering a region with sensors. Many different definitions of coverage exist depending on the goal of the coverage. In this paper, we address the problem of covering lines in a bounded rectangular region R by a set of sensors. We first introduce two new metrics, smallest k-covered line segment and longest k-uncovered line segment, for measuring the quality of line coverage achieved by a sensor deployment. Polynomial time algorithms are then proposed for finding the smallest k-covered axis-parallel line segment and the longest k-uncovered axis-parallel line segment in a bounded rectangular region R.