Online Routing in Convex Subdivisions
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.
KeywordsRandom Walk Plane Graph Competitive Ratio Delaunay Triangulation Link Distance
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- 2.A. Borodin and R. El-Yaniv. Online Computation and Competitive Analysis. Cambridge University Press, 1998.Google Scholar
- 3.P. Bose and P. Morin. Online routing in triangulations. In Proceedings of the Tenth International Symposium on Algorithms and Computation (ISAAC’99), volume 1741 of Springer LNCS, pages 113–122, 1999.Google Scholar
- 4.P. Bose and P. Morin. Competitive routing algorithms for greedy and minimum-weight triangulations. Manuscript, 2000.Google Scholar
- 8.E. Kranakis, H. Singh, and J. Urrutia. Compass routing on geometric networks. In Proceedings of the 11th Canadian Conference on Computational Geometry (CCCG’99), 1999.Google Scholar
- 10.F. P. Preparata and M. I. Shamos. Computational Geometry. Springer-Verlag, New York, 1985.Google Scholar