TY - GEN

T1 - Approximation algorithms for capacitated rectangle stabbing

AU - Even, Guy

AU - Rawitz, Dror

AU - Shahar, Shimon

PY - 2006

Y1 - 2006

N2 - In the rectangle stabbing problem we are given a set of axis parallel rectangles and a set of horizontal and vertical lines, and our goal is to find a minimum size subset of lines that intersect all the rectangles. We study the capacitated version of this problem in which the input includes an integral capacity for each line that bounds the number of rectangles that the line can cover. We consider two versions of this problem. In the first, one is allowed to use only a single copy of each line (hard capacities), and in the second, one is allowed to use multiple copies of every line provided that multiplicities are counted in the size of the solution (soft capacities). For the case of d-dimensional rectangle stabbing with soft capacities, we present a 6d-approximation algorithm and a 2-approximation algorithm when d = 1. For the case of hard capacities, we present a bi-criteria algorithm that computes 16d-approximate solutions that use at most two copies of every line. For the one dimensional case, an 8-approximation algorithm for hard capacities is presented.

AB - In the rectangle stabbing problem we are given a set of axis parallel rectangles and a set of horizontal and vertical lines, and our goal is to find a minimum size subset of lines that intersect all the rectangles. We study the capacitated version of this problem in which the input includes an integral capacity for each line that bounds the number of rectangles that the line can cover. We consider two versions of this problem. In the first, one is allowed to use only a single copy of each line (hard capacities), and in the second, one is allowed to use multiple copies of every line provided that multiplicities are counted in the size of the solution (soft capacities). For the case of d-dimensional rectangle stabbing with soft capacities, we present a 6d-approximation algorithm and a 2-approximation algorithm when d = 1. For the case of hard capacities, we present a bi-criteria algorithm that computes 16d-approximate solutions that use at most two copies of every line. For the one dimensional case, an 8-approximation algorithm for hard capacities is presented.

UR - http://www.scopus.com/inward/record.url?scp=33746086322&partnerID=8YFLogxK

U2 - 10.1007/11758471_5

DO - 10.1007/11758471_5

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AN - SCOPUS:33746086322

SN - 354034375X

SN - 9783540343752

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

SP - 18

EP - 29

BT - Algorithms and Complexity - 6th Italian Conference, CIAC 2006, Proceedings

PB - Springer Verlag

T2 - 6th Italian Conference on Algorithms and Complexity, CIAC 2006

Y2 - 29 May 2006 through 31 May 2006

ER -