2016/08/31 by Nicolas Bonichon, Prosenjit Bose, Bonichon, Nicolas +9
Computer Science · #Advanced Graph Theory Research #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #Graph Labeling and Dimension Problems
paper · doi:10.48550/arxiv.1608.08892
openalex publication_date 2016/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 angle-monotone---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.