Improved Routing on the Delaunay Triangulation

A geometric graph G = ( P , E ) is a set of points P in the plane and a set E of edges between pairs of points, where the weight of an edge is equal to the Euclidean distance between its two endpoints. In local routing we find a path in G from a source vertex s to a destination vertex t , using only knowledge of the current vertex, its incident edges, and the locations of s and t . We present an algorithm for local routing on the Delaunay triangulation, and show that it finds a path between a source vertex s and a target vertex t that is not longer than 3.56 | s t | , improving the previous bound of 5.9 | s t | .