Gabriel Triangulations and AngleMonotone Graphs: Local Routing and RecognitionBonichon, Nicolas and Bose, Prosenjit and Carmi, Paz and Kostitsyna, Irina and Lubiw, Anna and Verdonschot, Sander Gabriel Triangulations and AngleMonotone Graphs: Local Routing and Recognition. In: Graph Drawing and Network Visualization. GD 2016, September, 19.  21., 2016 , pp. 519531(Official URL: http://dx.doi.org/10.1007/9783319501062_40). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783319501062_40
AbstractA geometric graph is anglemonotone if every pair of vertices has a path between them that—after some rotation—is x and ymonotone. Anglemonotone graphs are √2spanners and they are increasingchord graphs. Dehkordi, Frati, and Gudmundsson introduced anglemonotone graphs in 2014 and proved that Gabriel triangulations are anglemonotone graphs. We give a polynomial time algorithm to recognize anglemonotone geometric graphs. We prove that every point set has a plane geometric graph that is generalized anglemonotone—specifically, we prove that the halfθ6graph is generalized anglemonotone. 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.
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