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

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	Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019)
Publisher	Springer, Cham
Pages	101-113
DOIs	https://doi.org/10.1007/978-3-030-35802-0_8
Publication status	Published - 2019

Publication series

Name	LNCS
Volume	11904

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 Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019) (pp. 101-113). (LNCS; Vol. 11904). Springer, Cham. 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; Kynčl, Jan; Mulzer, Wolfgang; Parada, Irene; Pilz, Alexander; Scheucher, Manfred; Valtr, Pavel; Vogtenhuber, Birgit; Welzl, Emo.

Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019). Springer, Cham, 2019. p. 101-113 (LNCS; 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 Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019). LNCS, vol. 11904, Springer, Cham, pp. 101-113. https://doi.org/10.1007/978-3-030-35802-0_8

Aichholzer, Oswin ; Balko, Martin ; Hoffmann, Michael ; Kynčl, Jan ; Mulzer, Wolfgang ; Parada, Irene ; Pilz, Alexander ; Scheucher, Manfred ; Valtr, Pavel ; Vogtenhuber, Birgit ; Welzl, Emo. / Minimal Representations of Order Types by Geometric Graphs. Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019). Springer, Cham, 2019. pp. 101-113 (LNCS).

@inproceedings{5be58fc098b840f18618ead335b2fd61,

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.",

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",

year = "2019",

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

language = "English",

series = "LNCS",

publisher = "Springer, Cham",

pages = "101--113",

booktitle = "Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019)",

}

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

Y1 - 2019

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.

UR - https://doi.org/10.1007/978-3-030-35802-0_8

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

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

M3 - Conference paper

T3 - LNCS

SP - 101

EP - 113

BT - Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019)

PB - Springer, Cham

ER -

Minimal Representations of Order Types by Geometric Graphs

Abstract

Publication series

Access to Document

Other files and links

Fingerprint

Cite this