@inproceedings{90affb9a36d447b0bb94d0d0acd29cfd,

title = "Gabriel triangulations and angle-monotone graphs: Local routing and recognition",

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 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.",

author = "Nicolas Bonichon and Prosenjit Bose and Paz Carmi and Irina Kostitsyna and Anna Lubiw and Sander Verdonschot",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG 2016.; 24th International Symposium on Graph Drawing and Network Visualization, GD 2016 ; Conference date: 19-09-2016 Through 21-09-2016",

year = "2016",

month = jan,

day = "1",

doi = "10.1007/978-3-319-50106-2_40",

language = "English",

isbn = "9783319501055",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "519--531",

editor = "Martin Nollenburg and Yifan Hu",

booktitle = "Graph Drawing and Network Visualization - 24th International Symposium, GD 2016, Revised Selected Papers",

address = "Germany",

}