Gabriel triangulations and angle-monotone graphs: Local routing and recognition
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.
|Series||Lecture Notes in Computer Science|
Bonichon, N. (Nicolas), Bose, P, Carmi, P. (Paz), Kostitsyna, I. (Irina), Lubiw, A. (Anna), & Verdonschot, S. (Sander). (2016). Gabriel triangulations and angle-monotone graphs: Local routing and recognition. In Lecture Notes in Computer Science. doi:10.1007/978-3-319-50106-2_40