Gabriel三角剖分与角单调图：局部路由与识别
Gabriel Triangulations and Angle-Monotone Graphs: Local Routing and Recognition
摘要：
一个几何图是角单调的，如果每对顶点之间有一条路径，经过一定的旋转后，该路径是$x$ -和$y$ -单调的。角单调图是$\sqrt 2$ -图，是增弦图. Dehkordi，Frati和Gudmundsson在2014年引入了角单调图，并证明了Gabriel三角剖分是角单调图。本文给出了一个多项式时间算法来识别角单调几何图。证明了每个点集都有一个广义角单调的平面几何图，具体地说，证明了半$θ_6$图是广义角单调的。我们给出了一个加布里埃尔三角形的局部路由算法，找到一条路径从任何顶点$s$到任何顶点$t$的长度是在$1 + \sqrt 2$倍的欧氏距离从$s$到$t$。最后，我们证明了一些下界和加布里埃尔三角形的局部路由算法的限制。
英文摘要：
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-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-$θ_6$-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 $1 + \sqrt 2$ times the Euclidean distance from $s$ to $t$. Finally, we prove some lower bounds and limits on local routing algorithms on Gabriel triangulations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
