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Gabriel triangulations and angle-monotone graphs: Local routing and recognition

par Bonichon, Nicolas;Bose, Prosenjit ;Carmi, Paz;Kostitsyna, Irina ;Lubiw, Anna;Verdonschot, Sander
Référence Lecture notes in computer science, 9801 LNCS, page (519-531)
Publication Publié, 2016

Article révisé par les pairs

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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 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.