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 contribution

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

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

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Aichholzer, O., Balko, M., Hoffmann, M., Kynčl, J., Mulzer, W., Parada, I., ... 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 contribution

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).

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