Minimal Representations of Order Types by Geometric Graphs

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

doi:10.1007/978-3-030-35802-0_8

Minimal Representations of Order Types by Geometric Graphs

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

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

4 Scopus citations

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 unequivocally 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. Exit edges have a natural dual characterization, which allows us to efficiently compute them and to bound their number.

Original language	English
Title of host publication	Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings
Editors	Daniel Archambault, Csaba D. Tóth
Publisher	Springer
Pages	101-113
Number of pages	13
ISBN (Print)	9783030358013
DOIs	https://doi.org/10.1007/978-3-030-35802-0_8
State	Published - 1 Jan 2019
Externally published	Yes
Event	27th International Symposium on Graph Drawing and Network Visualization, GD 2019 - Prague, Czech Republic Duration: 17 Sep 2019 → 20 Sep 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11904 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	27th International Symposium on Graph Drawing and Network Visualization, GD 2019
Country/Territory	Czech Republic
City	Prague
Period	17/09/19 → 20/09/19

Keywords

Geometric graph
Order type
Pseudoline arrangement
Straight-line drawing
Triangular cell

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-030-35802-0_8

Cite this

Aichholzer, O., Balko, M., Hoffmann, M., Kynčl, J., Mulzer, W., Parada, I., Pilz, A., Scheucher, M., Valtr, P., Vogtenhuber, B., & Welzl, E. (2019). Minimal Representations of Order Types by Geometric Graphs. In D. Archambault, & C. D. Tóth (Eds.), Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings (pp. 101-113). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11904 LNCS). Springer. https://doi.org/10.1007/978-3-030-35802-0_8

Aichholzer, Oswin ; Balko, Martin ; Hoffmann, Michael et al. / Minimal Representations of Order Types by Geometric Graphs. Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings. editor / Daniel Archambault ; Csaba D. Tóth. Springer, 2019. pp. 101-113 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{f170bb6445de4d02a0eee80827542609,

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 unequivocally 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. Exit edges have a natural dual characterization, which allows us to efficiently compute them and to bound their number.",

keywords = "Geometric graph, Order type, Pseudoline arrangement, Straight-line drawing, Triangular cell",

author = "Oswin Aichholzer and Martin Balko and Michael Hoffmann and Jan Kyn{\v c}l and Wolfgang Mulzer and Irene Parada and Alexander Pilz and Manfred Scheucher and Pavel Valtr and Birgit Vogtenhuber and Emo Welzl",

note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2019.; 27th International Symposium on Graph Drawing and Network Visualization, GD 2019 ; Conference date: 17-09-2019 Through 20-09-2019",

year = "2019",

month = jan,

day = "1",

doi = "10.1007/978-3-030-35802-0\_8",

language = "English",

isbn = "9783030358013",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer",

pages = "101--113",

editor = "Daniel Archambault and T{\'o}th, \{Csaba D.\}",

booktitle = "Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings",

address = "Germany",

}

Aichholzer, O, Balko, M, Hoffmann, M, Kynčl, J, Mulzer, W, Parada, I, Pilz, A, Scheucher, M, Valtr, P, Vogtenhuber, B & Welzl, E 2019, Minimal Representations of Order Types by Geometric Graphs. in D Archambault & CD Tóth (eds), Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11904 LNCS, Springer, pp. 101-113, 27th International Symposium on Graph Drawing and Network Visualization, GD 2019, Prague, Czech Republic, 17/09/19. https://doi.org/10.1007/978-3-030-35802-0_8

Minimal Representations of Order Types by Geometric Graphs. / Aichholzer, Oswin; Balko, Martin; Hoffmann, Michael et al.
Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings. ed. / Daniel Archambault; Csaba D. Tóth. Springer, 2019. p. 101-113 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11904 LNCS).

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

TY - GEN

T1 - Minimal Representations of Order Types by Geometric Graphs

AU - Aichholzer, Oswin

AU - Balko, Martin

AU - Hoffmann, Michael

AU - Kynčl, Jan

AU - Mulzer, Wolfgang

AU - Parada, Irene

AU - Pilz, Alexander

AU - Scheucher, Manfred

AU - Valtr, Pavel

AU - Vogtenhuber, Birgit

AU - Welzl, Emo

PY - 2019/1/1

Y1 - 2019/1/1

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 unequivocally 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. 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 unequivocally 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. Exit edges have a natural dual characterization, which allows us to efficiently compute them and to bound their number.

KW - Geometric graph

KW - Order type

KW - Pseudoline arrangement

KW - Straight-line drawing

KW - Triangular cell

UR - https://www.scopus.com/pages/publications/85076879629

U2 - 10.1007/978-3-030-35802-0_8

DO - 10.1007/978-3-030-35802-0_8

M3 - Conference contribution

AN - SCOPUS:85076879629

SN - 9783030358013

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 101

EP - 113

BT - Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings

A2 - Archambault, Daniel

A2 - Tóth, Csaba D.

PB - Springer

T2 - 27th International Symposium on Graph Drawing and Network Visualization, GD 2019

Y2 - 17 September 2019 through 20 September 2019

ER -

Aichholzer O, Balko M, Hoffmann M, Kynčl J, Mulzer W, Parada I et al. Minimal Representations of Order Types by Geometric Graphs. In Archambault D, Tóth CD, editors, Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings. Springer. 2019. p. 101-113. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-35802-0_8

Minimal Representations of Order Types by Geometric Graphs

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this