On piercing sets of axis-parallel rectangles and rings

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

10 Scopus citations

Abstract

We consider the p-piercing problem for axis-parallel rectangles. We are given a collection of axis-paxallel rectangles in the plane, and wish to determine whether there exists a set of p points whose union intersects all the given rectangles. We present efficient algorithms for finding a piercing set (i.e., a set of p points as above) for values of p = 1,2, 3, 4,5. The result for 4 and 5-piercing improves an existing result of O(n log3 n) and O(n log4n) to O(n log n) time, and is applied to find a better rectilinear 5-center agorithm. We improve the existing algorithm for general (but fixed) p, and we also extend our algorithms to higher dimensional space. We also consider the problem of piercing a set of rectaJagular rings.

Original languageEnglish
Title of host publicationAlgorithms - ESA 1997 - 5th Annual European Symposium, Proceedings
EditorsRainer Burkard, Gerhard Woeginger
PublisherSpringer Verlag
Pages430-442
Number of pages13
ISBN (Print)3540633979, 9783540633976
DOIs
StatePublished - 1 Jan 1997
Event5th Annual European Symposium on Algorithms, ESA 1997 - Graz, Austria
Duration: 15 Sep 199717 Sep 1997

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1284
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference5th Annual European Symposium on Algorithms, ESA 1997
Country/TerritoryAustria
CityGraz
Period15/09/9717/09/97

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