Minimum vertex cover in rectangle graphs

Reuven Bar-Yehuda; Danny Hermelin; Dror Rawitz

doi:10.1016/j.comgeo.2011.03.002

Minimum vertex cover in rectangle graphs

Reuven Bar-Yehuda
, Danny Hermelin
, Dror Rawitz

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We consider the Minimum Vertex Cover problem in intersection graphs of axis-parallel rectangles on the plane. We present two algorithms: The first is an EPTAS for non-crossing rectangle families, rectangle families R where R ¹R² is connected for every pair of rectangles R ¹,R²εR. This algorithm extends to intersection graphs of pseudo-disks. The second algorithm achieves a factor of (1.5+ε) in general rectangle families, for any fixed ε>0, and works also for the weighted variant of the problem. Both algorithms exploit the plane properties of axis-parallel rectangles in a novel way.

Original language	English
Pages (from-to)	356-364
Number of pages	9
Journal	Computational Geometry: Theory and Applications
Volume	44
Issue number	6-7
DOIs	https://doi.org/10.1016/j.comgeo.2011.03.002
State	Published - 1 Aug 2011
Externally published	Yes

Keywords

Approximation algorithms
Arrangement graphs
Axis-parallel rectangles
Intersection graphs
Pseudo-disks

ASJC Scopus subject areas

Computer Science Applications
Geometry and Topology
Control and Optimization
Computational Theory and Mathematics
Computational Mathematics

Access to Document

10.1016/j.comgeo.2011.03.002

Cite this

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title = "Minimum vertex cover in rectangle graphs",

abstract = "We consider the Minimum Vertex Cover problem in intersection graphs of axis-parallel rectangles on the plane. We present two algorithms: The first is an EPTAS for non-crossing rectangle families, rectangle families R where R 1R2 is connected for every pair of rectangles R 1,R2εR. This algorithm extends to intersection graphs of pseudo-disks. The second algorithm achieves a factor of (1.5+ε) in general rectangle families, for any fixed ε>0, and works also for the weighted variant of the problem. Both algorithms exploit the plane properties of axis-parallel rectangles in a novel way.",

keywords = "Approximation algorithms, Arrangement graphs, Axis-parallel rectangles, Intersection graphs, Pseudo-disks",

author = "Reuven Bar-Yehuda and Danny Hermelin and Dror Rawitz",

note = "Funding Information: We thank Victoria Barrientes, Kelly Benoit, Colleen Hainfeld, Melissa Walker, Mindy Sobota and Mark Sanderson for assistance in field work. Kelly Benoit first identified the tadpole's behavioral response to vocalizing male bullfrogs. We thank James and Robin Harper for permission to conduct experiments on their land. This research was supported by NIH grant NS-28565 (AMS) and an NSF Graduate Fellowship (SBH). Experimental protocols were approved by the Brown University IACUC.",

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doi = "10.1016/j.comgeo.2011.03.002",

language = "English",

volume = "44",

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journal = "Computational Geometry: Theory and Applications",

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publisher = "Elsevier B.V.",

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T1 - Minimum vertex cover in rectangle graphs

AU - Bar-Yehuda, Reuven

AU - Hermelin, Danny

AU - Rawitz, Dror

N1 - Funding Information: We thank Victoria Barrientes, Kelly Benoit, Colleen Hainfeld, Melissa Walker, Mindy Sobota and Mark Sanderson for assistance in field work. Kelly Benoit first identified the tadpole's behavioral response to vocalizing male bullfrogs. We thank James and Robin Harper for permission to conduct experiments on their land. This research was supported by NIH grant NS-28565 (AMS) and an NSF Graduate Fellowship (SBH). Experimental protocols were approved by the Brown University IACUC.

PY - 2011/8/1

Y1 - 2011/8/1

N2 - We consider the Minimum Vertex Cover problem in intersection graphs of axis-parallel rectangles on the plane. We present two algorithms: The first is an EPTAS for non-crossing rectangle families, rectangle families R where R 1R2 is connected for every pair of rectangles R 1,R2εR. This algorithm extends to intersection graphs of pseudo-disks. The second algorithm achieves a factor of (1.5+ε) in general rectangle families, for any fixed ε>0, and works also for the weighted variant of the problem. Both algorithms exploit the plane properties of axis-parallel rectangles in a novel way.

AB - We consider the Minimum Vertex Cover problem in intersection graphs of axis-parallel rectangles on the plane. We present two algorithms: The first is an EPTAS for non-crossing rectangle families, rectangle families R where R 1R2 is connected for every pair of rectangles R 1,R2εR. This algorithm extends to intersection graphs of pseudo-disks. The second algorithm achieves a factor of (1.5+ε) in general rectangle families, for any fixed ε>0, and works also for the weighted variant of the problem. Both algorithms exploit the plane properties of axis-parallel rectangles in a novel way.

KW - Approximation algorithms

KW - Arrangement graphs

KW - Axis-parallel rectangles

KW - Intersection graphs

KW - Pseudo-disks

UR - https://www.scopus.com/pages/publications/79953238832

U2 - 10.1016/j.comgeo.2011.03.002

DO - 10.1016/j.comgeo.2011.03.002

M3 - Article

AN - SCOPUS:79953238832

SN - 0925-7721

VL - 44

SP - 356

EP - 364

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

IS - 6-7

ER -

Minimum vertex cover in rectangle graphs

Abstract

Keywords

ASJC Scopus subject areas

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