TY - GEN

T1 - Multi cover of a polygon minimizing the sum of areas

AU - Abu-Affash, A. Karim

AU - Carmi, Paz

AU - Katz, Matthew J.

AU - Morgenstern, Gila

PY - 2011/3/9

Y1 - 2011/3/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79952258124&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-19094-0_15

DO - 10.1007/978-3-642-19094-0_15

M3 - Conference contribution

AN - SCOPUS:79952258124

SN - 9783642190933

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 134

EP - 145

BT - WALCOM

T2 - 5th Annual Workshop on Algorithms and Computation, WALCOM 2011

Y2 - 18 February 2011 through 20 February 2011

ER -