On piercing sets of axis-parallel rectangles and rings

Michael Segal

doi:10.1007/3-540-63397-9_33

On piercing sets of axis-parallel rectangles and rings

Michael Segal

Department of Communication Systems Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-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 language	English
Title of host publication	Algorithms - ESA 1997 - 5th Annual European Symposium, Proceedings
Editors	Rainer Burkard, Gerhard Woeginger
Publisher	Springer Verlag
Pages	430-442
Number of pages	13
ISBN (Print)	3540633979, 9783540633976
DOIs	https://doi.org/10.1007/3-540-63397-9_33
State	Published - 1 Jan 1997
Event	5th Annual European Symposium on Algorithms, ESA 1997 - Graz, Austria Duration: 15 Sep 1997 → 17 Sep 1997

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1284
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	5th Annual European Symposium on Algorithms, ESA 1997
Country/Territory	Austria
City	Graz
Period	15/09/97 → 17/09/97

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science (all)

Access to Document

10.1007/3-540-63397-9_33

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Segal, M. (1997). On piercing sets of axis-parallel rectangles and rings. In R. Burkard, & G. Woeginger (Eds.), Algorithms - ESA 1997 - 5th Annual European Symposium, Proceedings (pp. 430-442). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1284). Springer Verlag. https://doi.org/10.1007/3-540-63397-9_33

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Segal, M 1997, On piercing sets of axis-parallel rectangles and rings. in R Burkard & G Woeginger (eds), Algorithms - ESA 1997 - 5th Annual European Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1284, Springer Verlag, pp. 430-442, 5th Annual European Symposium on Algorithms, ESA 1997, Graz, Austria, 15/09/97. https://doi.org/10.1007/3-540-63397-9_33

On piercing sets of axis-parallel rectangles and rings. / Segal, Michael.

Algorithms - ESA 1997 - 5th Annual European Symposium, Proceedings. ed. / Rainer Burkard; Gerhard Woeginger. Springer Verlag, 1997. p. 430-442 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1284).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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On piercing sets of axis-parallel rectangles and rings

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