Online Routing in Triangulations

We consider online routing algorithms for routing between the vertices of embedded planar straight line graphs. Our results include (1) two deterministic memoryless routing algorithms, one that works for all Delaunay triangulations and the other that works for all regular triangulations, (2) a randomized memoryless algorithm that works for all triangulations, (3) an O(1) memory algorithm that works for all convex subdivisions, (4) an O(1) memory algorithm that approximates the shortest path in Delaunay triangulations, and (5) theoretical and experimental results on the competitiveness of these algorithms.