We consider online routing algorithms for finding paths between the vertices of plane graphs. Although it has been shown in Bose et al. (Internat. J. Comput. Geom. 12(4) (2002) 283) that there exists no competitive routing scheme that works on all triangulations, we show that there exists a simple online O(1)-memory c-competitive routing strategy that approximates the shortest path in triangulations possessing the diamond property, i.e., the total distance travelled by the algorithm to route a message between two vertices is at most a constant c times the shortest path. Our results imply a competitive routing strategy for certain classical triangulations such as the Delaunay, greedy, or minimum-weight triangulation, since they all possess the diamond property. We then generalize our results to show that the O(1)-memory c-competitive routing strategy works for all plane graphs possessing both the diamond property and the good convex polygon property.

Additional Metadata
Keywords Competitive routing, Delaunay triangulation, Geometric graph, Good polygon, Greedy triangulation, Minimum weight triangulation, Online routing, Planar graph, Spanner, Spanning ratio
Persistent URL dx.doi.org/10.1016/j.tcs.2004.05.019
Journal Theoretical Computer Science
Bose, P, & Morin, P. (2004). Competitive online routing in geometric graphs. Theoretical Computer Science, 324(2-3 SPEC. ISS.), 273–288. doi:10.1016/j.tcs.2004.05.019