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- W4298436291 abstract "We present a deterministic local routing algorithm that is guaranteed to find a path between any pair of vertices in a half-$theta_6$-graph (the half-$theta_6$-graph is equivalent to the Delaunay triangulation where the empty region is an equilateral triangle). The length of the path is at most $5/sqrt{3} approx 2.887$ times the Euclidean distance between the pair of vertices. Moreover, we show that no local routing algorithm can achieve a better routing ratio, thereby proving that our routing algorithm is optimal. This is somewhat surprising because the spanning ratio of the half-$theta_6$-graph is 2, meaning that even though there always exists a path whose lengths is at most twice the Euclidean distance, we cannot always find such a path when routing locally. Since every triangulation can be embedded in the plane as a half-$theta_6$-graph using $O(log n)$ bits per vertex coordinate via Schnyder's embedding scheme (SODA 1990), our result provides a competitive local routing algorithm for every such embedded triangulation. Finally, we show how our routing algorithm can be adapted to provide a routing ratio of $15/sqrt{3} approx 8.660$ on two bounded degree subgraphs of the half-$theta_6$-graph." @default.
- W4298436291 created "2022-10-02" @default.
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- W4298436291 date "2014-09-22" @default.
- W4298436291 modified "2023-10-14" @default.
- W4298436291 title "Optimal local routing on Delaunay triangulations defined by empty equilateral triangles" @default.
- W4298436291 doi "https://doi.org/10.48550/arxiv.1409.6397" @default.
- W4298436291 hasPublicationYear "2014" @default.
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