We consider online routing algorithms for finding paths between the vertices of plane graphs. We show (1) there exists a routing algorithm for arbitrary triangulations that has no memory and uses no randomization, (2) no equivalent result is possible for convex subdivisions, (3) there is no competitive online routing algorithm under the Euclidean distance metric in arbitrary triangulations, and (4) there is no competitive online routing algorithm under the link distance metric even when the input graph is restricted to be a Delaunay, greedy, or minimum-weight triangulation.

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doi.org/10.1142/S021819590200089X
International Journal of Computational Geometry and Applications
School of Computer Science

Bose, P, Brodnik, A. (Andrej), Carlsson, S. (Svante), Demaine, E.D. (Erik D.), Fleischer, R. (Rudolf), López-Ortiz, A. (Alejandro), … Munro, J.I. (J. Ian). (2002). Online routing in convex subdivisions. In International Journal of Computational Geometry and Applications (Vol. 12, pp. 283–295). doi:10.1142/S021819590200089X