Delaunay graphs are almost as good as complete graphs
Discrete & Computational Geometry
Theoretical Computer Science
Information and Computation
Constructing competitive tours from local information
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
Online computation and competitive analysis
Online computation and competitive analysis
Which Triangulations Approximate the Complete Graph?
Proceedings of the International Symposium on Optimal Algorithms
Constructing Plane Spanners of Bounded Degree and Low Weight
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
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Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Augmenting the connectivity of geometric graphs
Computational Geometry: Theory and Applications
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INFOCOM'10 Proceedings of the 29th conference on Information communications
Almost all Delaunay triangulations have stretch factor greater than π/2
Computational Geometry: Theory and Applications
Compact routing for graphs excluding a fixed minor
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Online multi-path routing in a maze
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
The stretch factor of L1- and L∞-delaunay triangulations
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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International Journal of Artificial Life Research
Proceedings of the fourteenth ACM international symposium on Mobile ad hoc networking and computing
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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.