Competitive Routing on a Bounded-Degree Plane Spanner

We show that it is possible to route locally and competitively on two bounded-degree plane 6-spanners, one with maximum degree 12 and the other with maximum degree 9. Both spanners are subgraphs of the empty equilateral triangle Delaunay triangulation. First, in a weak routing model where the only information stored at each vertex is its neighbourhood, we show how to find a path between any two vertices of a 6-spanner of maximum degree 12, such that the path has length at most 95/ √ 3 times the straight-line distance between the vertices. In a slightly stronger model, where in addition to the neighbourhood of each vertex, we store O(1) additional information, we show how to find a path that has length at most 15/ √ 3 times the Euclidean distance both in a 6-spanner of maximum degree 12 and a 6-spanner of maximum degree 9.