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Communication Dans Un Congrès Année : 2016

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

Résumé

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.

Dates et versions

hal-01412047 , version 1 (07-12-2016)

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Nicolas Bonichon, Prosenjit Bose, Paz Carmi, Irina Kostitsyna, Anna Lubiw, et al.. Gabriel Triangulations and Angle-Monotone Graphs: Local Routing and Recognition. Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016), Sep 2016, Athènes, Greece. ⟨hal-01412047⟩

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