Approximation Algorithm for Line Segment Coverage for Wireless Sensor Network

TL;DR

This paper addresses the NP-hard problem of covering line segments in wireless sensor networks by proposing a constant factor approximation algorithm and demonstrating the existence of a PTAS for axis-parallel segments.

Contribution

It introduces a constant factor approximation algorithm and proves the existence of a PTAS for covering axis-parallel line segments in sensor networks.

Findings

NP-hardness of the line segment coverage problem

Proposed a constant factor approximation algorithm

Established the existence of a PTAS for the problem

Abstract

The coverage problem in wireless sensor networks deals with the problem of covering a region or parts of it with sensors. In this paper, we address the problem of covering a set of line segments in sensor networks. A line segment ` is said to be covered if it intersects the sensing regions of at least one sensor distributed in that region. We show that the problem of finding the minimum number of sensors needed to cover each member in a given set of line segments in a rectangular area is NP-hard. Next, we propose a constant factor approximation algorithm for the problem of covering a set of axis-parallel line segments. We also show that a PTAS exists for this problem.