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Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms

Competitive Routing in the Half-θ6-Graph

Abstract

We present a deterministic local routing scheme that is guaranteed to find a path between any pair of vertices in a half-θ6-graph whose length is at most 5/√3 = 2.886… times the Euclidean distance between the pair of vertices. The half-θ6-graph is identical to the Delaunay triangulation where the empty region is an equilateral triangle. Moreover, we show that no local routing scheme can achieve a better competitive spanning ratio thereby implying that our routing scheme is optimal. This is somewhat surprising because the spanning ratio of the half-θ6-graph is 2. Since every triangulation can be embedded in the plane as a half-θ6-graph using O(log n) bits per vertex coordinate via Schnyder's embedding scheme (SODA 1990), our result provides a competitive local routing scheme for every such embedded triangulation.

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cover image Proceedings
Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms
Pages: 1319 - 1328
Editor: Yuval Rabani, The Hebrew Institute of Jerusalem, Jerusalem, Israel
ISBN (Print): 978-1-61197-210-8
ISBN (Online): 978-1-61197-309-9

History

Published online: 18 December 2013

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*
Research supported in part by NSERC and the Danish Council for Independent Research, Natural Sciences.

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