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.