A memoryless routing algorithm is one in which the decision about the next edge on the route to a vertex t for a packet currently located at vertex v is made based only on the coordinates of v, t, and the neighborhood, N(v), of v. The current paper explores the limitations of such algorithms by showing that, for any (randomized) memoryless routing algorithm A, there exists a convex subdivision on which A takes Ω(n 2) expected time to route a message between some pair of vertices. Since this lower bound is matched by a random walk, this result implies that the geometric information available in convex subdivisions does not reduce the worst-case routing time for this class of routing algorithms. The current paper also shows the existence of triangulations for which the Random-Compass algorithm proposed by Bose et al. (2002, 2004) requires 2 Ω(n) time to route between some pair of vertices.

Additional Metadata
Keywords Geometric routing, Lower bounds, Routing
Persistent URL dx.doi.org/10.1016/j.comgeo.2011.12.005
Journal Computational Geometry
Citation
Chen, D. (Dan), Devroye, L. (Luc), Dujmović, V, & Morin, P. (2012). Memoryless routing in convex subdivisions: Random walks are optimal. Computational Geometry, 45(4), 178–185. doi:10.1016/j.comgeo.2011.12.005