Online Routing in Triangulations

We consider online routing strategies for routing between the vertices of embedded planar straight line graphs. Our results include (1) two deterministic memoryless routing strategies, one that works for all Delaunay triangulations and the other that works for all regular triangulations, (2) a randomized memoryless strategy that works for all triangulations, (3) an O(1) memory strategy that works for all convex subdivisions, (4) an O(1) memory strategy that approximates the shortest path in Delaunay triangulations, and (5) theoretical and experimental results on the competitiveness of these strategies.

[1]  Mark de Berg,et al.  Simple traversal of a subdivision without extra storage , 1996, SCG '96.

[2]  V. Chvátal.  A combinatorial theorem in plane geometry , 1975 .

[3]  J. A. Bondy,et al.  Graph Theory with Applications , 1978 .

[4]  Ivan Stojmenovic,et al.  Routing with Guaranteed Delivery in Ad Hoc Wireless Networks , 1999, DIALM '99.

[5]  Carl Gutwin,et al.  Classes of graphs which approximate the complete euclidean graph , 1992, Discret. Comput. Geom..

[6]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .

[7]  David P. Dobkin,et al.  Delaunay graphs are almost as good as complete graphs , 1990, Discret. Comput. Geom..

[8]  Jorge Urrutia,et al.  Compass routing on geometric networks , 1999, CCCG.

[9]  G. Ziegler.  Lectures on Polytopes , 1994 .

[10]  C. Lawson.  Software for C1 Surface Interpolation , 1977 .

[11]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[12]  Atsuyuki Okabe,et al.  Spatial Tessellations: Concepts and Applications of Voronoi Diagrams , 1992, Wiley Series in Probability and Mathematical Statistics.

[13]  Herbert Edelsbrunner,et al.  An acyclicity theorem for cell complexes ind dimension , 1990, Comb..

[14]  Ricardo A. Baeza-Yates,et al.  Searching in the Plane , 1993, Inf. Comput..

[15]  Subir Kumar Ghosh,et al.  Optimal On-line Algorithms for Walking with Minimum Number of Turns in Unknown Streets , 1997, Comput. Geom..

[16]  Rolf Klein.  Walking an Unknown Street with Bounded Detour , 1991, Comput. Geom..

[17]  J. A. Bondy,et al.  Graph Theory with Applications , 1978 .

[18]  Rolf Klein,et al.  Searching for the kernel of a polygon—a competitive strategy , 1995, SCG '95.