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

^*Corresponding author for this work

Institute of Software Technology (7160)

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › 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 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
Subtitle of host publication	27th International Symposium, GD 2019, Prague, Czech Republic, September 17–20, 2019, Proceedings
Place of Publication	Cham
Publisher	Springer
Pages	101-113
ISBN (Electronic)	978-3-030-35802-0
ISBN (Print)	978-3-030-35801-3
DOIs	https://doi.org/10.1007/978-3-030-35802-0_8
Publication status	Published - 2019
Event	27th International Symposium on Graph Drawing and Network Visualization: GD 2019 - Hotel Floret, Pruhonice, Czech Republic Duration: 17 Sept 2019 → 20 Sept 2019 https://kam.mff.cuni.cz/gd2019/index.html https://kam.mff.cuni.cz/gd2019/

Publication series

Name	Lecture Notes in Computer Science
Volume	11904

Conference

Conference	27th International Symposium on Graph Drawing and Network Visualization
Abbreviated title	GD 2019
Country/Territory	Czech Republic
City	Pruhonice
Period	17/09/19 → 20/09/19
Internet address	https://kam.mff.cuni.cz/gd2019/index.html https://kam.mff.cuni.cz/gd2019/

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 Graph Drawing and Network Visualization : 27th International Symposium, GD 2019, Prague, Czech Republic, September 17–20, 2019, Proceedings (pp. 101-113). (Lecture Notes in Computer Science; Vol. 11904). Springer. 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, Prague, Czech Republic, September 17–20, 2019, Proceedings. Cham: Springer, 2019. p. 101-113 (Lecture Notes in Computer Science; Vol. 11904).

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

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 Graph Drawing and Network Visualization : 27th International Symposium, GD 2019, Prague, Czech Republic, September 17–20, 2019, Proceedings. Lecture Notes in Computer Science, vol. 11904, Springer, Cham, pp. 101-113, 27th International Symposium on Graph Drawing and Network Visualization, Pruhonice, Czech Republic, 17/09/19. https://doi.org/10.1007/978-3-030-35802-0_8

Aichholzer O, Balko M, Hoffmann M, Kynčl J, Mulzer W, Parada I et al. Minimal Representations of Order Types by Geometric Graphs. In Graph Drawing and Network Visualization : 27th International Symposium, GD 2019, Prague, Czech Republic, September 17–20, 2019, Proceedings. Cham: Springer. 2019. p. 101-113. (Lecture Notes in Computer Science). doi: 10.1007/978-3-030-35802-0_8

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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",

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

language = "English",

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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

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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.

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

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SN - 978-3-030-35801-3

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ER -

Minimal Representations of Order Types by Geometric Graphs

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