Extending Simple Drawings

Alan Arroyo, Martin Derka, Irene Parada

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem KonferenzbandForschungBegutachtung

Abstract

Simple drawings of graphs are those in which each pair of edges share at most one point, either a common endpoint or a proper crossing. In this paper we study the problem of extending a simple drawing D(G) of a graph G by inserting a set of edges from the complement of G into D(G) such that the result is a simple drawing. In the context of rectilinear drawings, the problem is trivial. For pseudolinear drawings, the existence of such an extension follows from Levi’s enlargement lemma. In contrast, we prove that deciding if a given set of edges can be inserted into a simple drawing is NP-complete. Moreover, we show that the maximization version of the problem is APX-hard. We also present a polynomial-time algorithm for deciding whether one edge uv can be inserted into D(G) when {u,v} is a dominating set for the graph G.
Originalspracheenglisch
TitelGraph Drawing and Network Visualization
Untertitel 27th International Symposium on Graph Drawing and Network Visualization (GD 2019), Proceedings
Herausgeber (Verlag)Springer, Cham
Seiten230-243
DOIs
PublikationsstatusVeröffentlicht - 2019
Veranstaltung27th International Symposium on Graph Drawing and Network Visualization - Hotel Floret, Pruhonice, Tschechische Republik
Dauer: 17 Sep 201920 Sep 2019
https://kam.mff.cuni.cz/gd2019/index.html
https://kam.mff.cuni.cz/gd2019/

Publikationsreihe

NameLNCS
Band11904

Konferenz

Konferenz27th International Symposium on Graph Drawing and Network Visualization
KurztitelGD 2019
LandTschechische Republik
OrtPruhonice
Zeitraum17/09/1920/09/19
Internetadresse

Fingerprint

Graph in graph theory
Enlargement
Dominating Set
Polynomial-time Algorithm
Drawing
Lemma
Trivial
Complement
NP-complete problem
Context

Dies zitieren

Arroyo, A., Derka, M., & Parada, I. (2019). Extending Simple Drawings. in Graph Drawing and Network Visualization : 27th International Symposium on Graph Drawing and Network Visualization (GD 2019), Proceedings (S. 230-243). (LNCS; Band 11904). Springer, Cham. https://doi.org/10.1007/978-3-030-35802-0_18

Extending Simple Drawings. / Arroyo, Alan; Derka, Martin; Parada, Irene.

Graph Drawing and Network Visualization : 27th International Symposium on Graph Drawing and Network Visualization (GD 2019), Proceedings. Springer, Cham, 2019. S. 230-243 (LNCS; Band 11904).

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem KonferenzbandForschungBegutachtung

Arroyo, A, Derka, M & Parada, I 2019, Extending Simple Drawings. in Graph Drawing and Network Visualization : 27th International Symposium on Graph Drawing and Network Visualization (GD 2019), Proceedings. LNCS, Bd. 11904, Springer, Cham, S. 230-243, Pruhonice, Tschechische Republik, 17/09/19. https://doi.org/10.1007/978-3-030-35802-0_18
Arroyo A, Derka M, Parada I. Extending Simple Drawings. in Graph Drawing and Network Visualization : 27th International Symposium on Graph Drawing and Network Visualization (GD 2019), Proceedings. Springer, Cham. 2019. S. 230-243. (LNCS). https://doi.org/10.1007/978-3-030-35802-0_18
Arroyo, Alan ; Derka, Martin ; Parada, Irene. / Extending Simple Drawings. Graph Drawing and Network Visualization : 27th International Symposium on Graph Drawing and Network Visualization (GD 2019), Proceedings. Springer, Cham, 2019. S. 230-243 (LNCS).
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AB - Simple drawings of graphs are those in which each pair of edges share at most one point, either a common endpoint or a proper crossing. In this paper we study the problem of extending a simple drawing D(G) of a graph G by inserting a set of edges from the complement of G into D(G) such that the result is a simple drawing. In the context of rectilinear drawings, the problem is trivial. For pseudolinear drawings, the existence of such an extension follows from Levi’s enlargement lemma. In contrast, we prove that deciding if a given set of edges can be inserted into a simple drawing is NP-complete. Moreover, we show that the maximization version of the problem is APX-hard. We also present a polynomial-time algorithm for deciding whether one edge uv can be inserted into D(G) when {u,v} is a dominating set for the graph G.

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