Multi cover of a polygon minimizing the sum of areas

A. Karim Abu-Affash, Paz Carmi, Matthew J. Katz, Gila Morgenstern

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

We consider a geometric optimization problem that arises in sensor network design. Given a polygon P (possibly with holes) with n vertices, a set Y of m points representing sensors, and an integer k, 1 ≤ k ≤ m. The goal is to assign a sensing range, r i , to each of the sensors y i ∈ Y, such that each point p ∈ P is covered by at least k sensors, and the cost, , of the assignment is minimized, where α is a constant. In this paper, we assume that α = 2, that is, find a set of disks centered at points of Y, such that (i) each point in P is covered by at least k disks, and (ii) the sum of the areas of the disks is minimized. We present, for any constant k ≥ 1, a polynomial-time c 1-approximation algorithm for this problem, where c 1 = c 1(k) is a constant. The discrete version, where one has to cover a given set of n points, X, by disks centered at points of Y, arises as a subproblem. We present a polynomial-time c 2-approximation algorithm for this problem, where c 2 = c 2(k) is a constant.

Original languageEnglish
Title of host publicationWALCOM
Subtitle of host publicationAlgorithms and Computation - 5th International Workshop, WALCOM 2011, Proceedings
Pages134-145
Number of pages12
DOIs
StatePublished - 9 Mar 2011
Event5th Annual Workshop on Algorithms and Computation, WALCOM 2011 - New Delhi, India
Duration: 18 Feb 201120 Feb 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6552 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference5th Annual Workshop on Algorithms and Computation, WALCOM 2011
Country/TerritoryIndia
CityNew Delhi
Period18/02/1120/02/11

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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