|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 $sqrt 2$-spanners and they are increasing hyp chord graphs.
Dehkordi, Frati, and Gudmundsson introduced angle-monotone graphs in 2014 and proved that Gabriel triangulations are anglehyp 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 hts 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 $1 + sqrt 2$ times the Euclidean distance from s to t.
Finally, we prove some lower bounds and limits on local routing algorithms on Gabriel triangulations. |