Piercing pairwise intersecting geodesic disks

Prosenjit Bose; Paz Carmi; Thomas C. Shermer

doi:10.1016/j.comgeo.2021.101774

Piercing pairwise intersecting geodesic disks

Prosenjit Bose, Paz Carmi, Thomas C. Shermer

Department of Computer Science

Ben-Gurion University of the Negev

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

Abstract

Given a simple polygon P on n vertices, n_r of which are reflex, and a set D of m pairwise intersecting geodesic disks in P, we show that at most 14 points in P suffice to pierce all the disks in D and these points can be computed in O(n+mlog⁡n_r) time.

Original language	American English
Article number	101774
Journal	Computational Geometry: Theory and Applications
Volume	98
DOIs	https://doi.org/10.1016/j.comgeo.2021.101774
State	Published - 1 Oct 2021

Keywords

Geodesic disk
Helly theorem
LP-type
Piercing set
Polygon

All Science Journal Classification (ASJC) codes

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

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10.1016/j.comgeo.2021.101774

Cite this

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title = "Piercing pairwise intersecting geodesic disks",

abstract = "Given a simple polygon P on n vertices, nr of which are reflex, and a set D of m pairwise intersecting geodesic disks in P, we show that at most 14 points in P suffice to pierce all the disks in D and these points can be computed in O(n+mlog⁡nr) time.",

keywords = "Geodesic disk, Helly theorem, LP-type, Piercing set, Polygon",

author = "Prosenjit Bose and Paz Carmi and Shermer, \{Thomas C.\}",

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year = "2021",

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doi = "10.1016/j.comgeo.2021.101774",

language = "American English",

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AU - Bose, Prosenjit

AU - Carmi, Paz

AU - Shermer, Thomas C.

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N2 - Given a simple polygon P on n vertices, nr of which are reflex, and a set D of m pairwise intersecting geodesic disks in P, we show that at most 14 points in P suffice to pierce all the disks in D and these points can be computed in O(n+mlog⁡nr) time.

AB - Given a simple polygon P on n vertices, nr of which are reflex, and a set D of m pairwise intersecting geodesic disks in P, we show that at most 14 points in P suffice to pierce all the disks in D and these points can be computed in O(n+mlog⁡nr) time.

KW - Geodesic disk

KW - Helly theorem

KW - LP-type

KW - Piercing set

KW - Polygon

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U2 - 10.1016/j.comgeo.2021.101774

DO - 10.1016/j.comgeo.2021.101774

M3 - Article

SN - 0925-7721

VL - 98

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

M1 - 101774

ER -

Piercing pairwise intersecting geodesic disks

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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