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Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms

On the Spanning and Routing Ratio of Theta-Four

Abstract

We present a routing algorithm for the Θ4-graph that computes a path between any two vertices s and t having length at most 17 times the Euclidean distance between s and t. To compute this path, at each step, the algorithm only uses knowledge of the location of the current vertex, its (at most four) outgoing edges, the destination vertex, and one additional bit of information in order to determine the next edge to follow. This provides the first known online, local, competitive routing algorithm with constant routing ratio for the Θ4-graph, as well as improving the best known upper bound on the spanning ratio of these graphs from 237 to 17. We also show that without this additional bit of information, the routing ratio increases to ≈ 17.03.

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cover image Proceedings
Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms
Pages: 2361 - 2370
Editor: Timothy M. Chan, University of Illinois at Urbana-Champaign, USA
ISBN (Online): 978-1-61197-548-2

History

Published online: 2 January 2019

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*
This work was partially supported by the National Sciences and Engineering Research Council of Canada (NSERC).

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