Minimal representations of order types by geometric graphs

Oswin Aichholzer; Martin Balko; Michael Hoffmann; Jan Kyncl; Wolfgang Mulzer; Irene Parada; Alexander Pilz; Manfred Scheucher; Pavel Valtr; Birgit Vogtenhuber; Emo Welzl

doi:10.7155/jgaa.00545

Minimal representations of order types by geometric graphs

Oswin Aichholzer, Martin Balko, Michael Hoffmann, Jan Kyncl, Wolfgang Mulzer, Irene Parada, Alexander Pilz, Manfred Scheucher, Pavel Valtr, Birgit Vogtenhuber, Emo Welzl

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

Abstract

In order to have a compact visualization of the order type of a given point set S, we are interested in geometric graphs on S with few edges that unambiguously display the order type of S. We introduce the concept of exit edges, which prevent the order type from changing under continuous motion of vertices. That is, in the geometric graph on S whose edges are the exit edges, in order to change the order type of S, at least one vertex needs to move across an exit edge. Exit edges have a natural dual characterization, which allows us to efficiently compute them and to bound their number.

Original language	English
Pages (from-to)	551-572
Number of pages	22
Journal	Journal of Graph Algorithms and Applications
Volume	24
Issue number	4
DOIs	https://doi.org/10.7155/jgaa.00545
Publication status	Published - Dec 2020

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Computer Science(all)
Computer Science Applications
Computational Theory and Mathematics

Fields of Expertise

Information, Communication & Computing

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10.7155/jgaa.00545Licence: CC BY 4.0

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title = "Minimal representations of order types by geometric graphs",

abstract = "In order to have a compact visualization of the order type of a given point set S, we are interested in geometric graphs on S with few edges that unambiguously display the order type of S. We introduce the concept of exit edges, which prevent the order type from changing under continuous motion of vertices. That is, in the geometric graph on S whose edges are the exit edges, in order to change the order type of S, at least one vertex needs to move across an exit edge. Exit edges have a natural dual characterization, which allows us to efficiently compute them and to bound their number.",

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AU - Aichholzer, Oswin

AU - Balko, Martin

AU - Hoffmann, Michael

AU - Kyncl, Jan

AU - Mulzer, Wolfgang

AU - Parada, Irene

AU - Pilz, Alexander

AU - Scheucher, Manfred

AU - Valtr, Pavel

AU - Vogtenhuber, Birgit

AU - Welzl, Emo

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Y1 - 2020/12

N2 - In order to have a compact visualization of the order type of a given point set S, we are interested in geometric graphs on S with few edges that unambiguously display the order type of S. We introduce the concept of exit edges, which prevent the order type from changing under continuous motion of vertices. That is, in the geometric graph on S whose edges are the exit edges, in order to change the order type of S, at least one vertex needs to move across an exit edge. Exit edges have a natural dual characterization, which allows us to efficiently compute them and to bound their number.

AB - In order to have a compact visualization of the order type of a given point set S, we are interested in geometric graphs on S with few edges that unambiguously display the order type of S. We introduce the concept of exit edges, which prevent the order type from changing under continuous motion of vertices. That is, in the geometric graph on S whose edges are the exit edges, in order to change the order type of S, at least one vertex needs to move across an exit edge. Exit edges have a natural dual characterization, which allows us to efficiently compute them and to bound their number.

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DO - 10.7155/jgaa.00545

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JO - Journal of Graph Algorithms and Applications

JF - Journal of Graph Algorithms and Applications

IS - 4

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Minimal representations of order types by geometric graphs

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