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 -