Gabriel triangulations and angle-monotone graphs: Local routing and recognition

Nicolas Bonichon, Prosenjit Bose, Paz Carmi, Irina Kostitsyna, Anna Lubiw, Sander Verdonschot

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

19 Scopus citations


A geometric graph is angle-monotone if every pair of vertices has a path between them that—after some rotation—is x- and y-monotone. Angle-monotone graphs are √2-spanners and they are increasing-chord graphs. Dehkordi, Frati, and Gudmundsson introduced angle-monotone graphs in 2014 and proved that Gabriel triangulations are angle-monotone graphs. We give a polynomial time algorithm to recognize angle-monotone geometric graphs. We prove that every point set has a plane geometric graph that is generalized anglemonotone— specifically, we prove that the half-θ6-graph is generalized angle-monotone. We give a local routing algorithm for Gabriel triangulations that finds a path from any vertex s to any vertex t whose length is within 1 + √ 2 times the Euclidean distance from s to t. Finally, we prove some lower bounds and limits on local routing algorithms on Gabriel triangulations.

Original languageEnglish
Title of host publicationGraph Drawing and Network Visualization - 24th International Symposium, GD 2016, Revised Selected Papers
EditorsMartin Nollenburg, Yifan Hu
PublisherSpringer Verlag
Number of pages13
ISBN (Print)9783319501055
StatePublished - 1 Jan 2016
Event24th International Symposium on Graph Drawing and Network Visualization, GD 2016 - Athens, Greece
Duration: 19 Sep 201621 Sep 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9801 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference24th International Symposium on Graph Drawing and Network Visualization, GD 2016

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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