Approximation Algorithms for Minimum Sum of Moving-Distance and Opening-Costs Target Coverage Problem

TL;DR

This paper introduces approximation algorithms for the MinMD+OCTC problem, which involves covering targets with mobile sensors while minimizing costs, providing optimal solutions for line targets and an approximation for plane targets.

Contribution

It presents the first polynomial-time optimal solution for line targets and an 8.928-approximation algorithm for plane targets in the MinMD+OCTC problem.

Findings

Optimal polynomial-time solution for targets on a line.

8.928-approximation algorithm for targets on a plane.

Effective cost minimization in target coverage with mobile sensors.

Abstract

In this paper, we study the Minimum Sum of Moving-Distance and Opening-Costs Target Coverage problem (MinMD$+$OCTC). Given a set of targets and a set of base stations on the plane, an opening cost function for every base station, the opened base stations can emit mobile sensors with a radius of $r$ from base station to cover the targets. The goal of MinMD$+$OCTC is to cover all the targets and minimize the sum of the opening cost and the moving distance of mobile sensors. We give the optimal solution in polynomial time for the MinMD$+$OCTC problem with targets on a straight line, and present a 8.928 approximation algorithm for a special case of the MinMD$+$OCTC problem with the targets on the plane.