TY - GEN

T1 - Gabriel triangulations and angle-monotone graphs

T2 - 24th International Symposium on Graph Drawing and Network Visualization, GD 2016

AU - Bonichon, Nicolas

AU - Bose, Prosenjit

AU - Carmi, Paz

AU - Kostitsyna, Irina

AU - Lubiw, Anna

AU - Verdonschot, Sander

N1 - Funding Information:
Funding acknowledgements: A.L. thanks NSERC (Natural Sciences and Engineering Council of Canada). S.V. thanks NSERC and the Ontario Ministry of Research and Innovation. N.B. thanks French National Research Agency (ANR) in the frame of the “Investments for the future” Programme IdEx Bordeaux - CPU (ANR-10-IDEX-03-02). I.K. was supported in part by the NWO under project no. 612.001.106, and by F.R.S.-FNRS.
Publisher Copyright:
© Springer International Publishing AG 2016.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85007387971&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-50106-2_40

DO - 10.1007/978-3-319-50106-2_40

M3 - Conference contribution

AN - SCOPUS:85007387971

SN - 9783319501055

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 519

EP - 531

BT - Graph Drawing and Network Visualization - 24th International Symposium, GD 2016, Revised Selected Papers

A2 - Nollenburg, Martin

A2 - Hu, Yifan

PB - Springer Verlag

Y2 - 19 September 2016 through 21 September 2016

ER -