1 research outputs found
Some Properties of Continuous Yao Graph
International audienceGiven a set S of points in the plane and an angle \theta p, q \in ScY (\theta )\theta 0h, is connected, where is the graph after removing all edges and points inside h from the graph . Also, we show that there is a set of n points in the plane and a convex region C such that for every , is not connected.Given a geometric network G and two vertices x and y of G, we call a path P from x to y a self-approaching path, if for any point q on P, when a point p moves continuously along the path from x to q, it always get closer to q. A geometric graph G is self-approaching, if for every pair of vertices x and y there exists a self-approaching path in G from x to y. In this paper, we show that there is a set P of n points in the plane such that for some angles , Yao graph on P with parameter is not a self-approaching graph. Instead, the corresponding continuous Yao graph on P is a self-approaching graph. Furthermore, in general, we show that for every , is not necessarily a self-approaching graph