Gabriel Triangulations and Angle-Monotone Graphs: Local Routing and Recognition

Bonichon, Nicolas and Bose, Prosenjit and Carmi, Paz and Kostitsyna, Irina and Lubiw, Anna and Verdonschot, Sander Gabriel Triangulations and Angle-Monotone Graphs: Local Routing and Recognition. In: Graph Drawing and Network Visualization. GD 2016, September, 19. - 21., 2016 , pp. 519-531(Official URL: http://dx.doi.org/10.1007/978-3-319-50106-2_40).

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Abstract

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.

Item Type: Conference Paper
Classifications: G Algorithms and Complexity > G.560 Geometry
P Styles > P.720 Straight-line
URI: http://gdea.informatik.uni-koeln.de/id/eprint/1567

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