Approximation algorithms for capacitated rectangle stabbing

Guy Even*, Dror Rawitz, Shimon Shahar

*Corresponding author for this work

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

Abstract

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.

Original languageEnglish
Title of host publicationAlgorithms and Complexity - 6th Italian Conference, CIAC 2006, Proceedings
PublisherSpringer Verlag
Pages18-29
Number of pages12
ISBN (Print)354034375X, 9783540343752
DOIs
StatePublished - 2006
Event6th Italian Conference on Algorithms and Complexity, CIAC 2006 - Rome, Italy
Duration: 29 May 200631 May 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3998 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference6th Italian Conference on Algorithms and Complexity, CIAC 2006
Country/TerritoryItaly
CityRome
Period29/05/0631/05/06

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