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Local Routing in Spanners Based on WSPDs

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Algorithms and Data Structures (WADS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10389))

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Abstract

The well-separated pair decomposition (WSPD) of the complete Euclidean graph defined on points in \(\mathbb {R}^2\) (Callahan and Kosaraju [JACM, 42 (1): 67-90, 1995]) is a technique for partitioning the edges of the complete graph based on length into a linear number of sets. Among the many different applications of WSPDs, Callahan and Kosaraju proved that the sparse subgraph that results by selecting an arbitrary edge from each set (called WSPD-spanner) is a \(1+8/(s-4)\)-spanner, where \(s>4\) is the separation ratio used for partitioning the edges.

Although competitive local-routing strategies exist for various spanners such as Yao-graphs, \(\varTheta \)-graphs, and variants of Delaunay graphs, few local-routing strategies are known for any WSPD-spanner. Our main contribution is a local-routing algorithm with a near-optimal competitive routing ratio of \(1+O(1/s)\) on a WSPD-spanner. Specifically, we present a 2-local and a 1-local routing algorithm on a WSPD-spanner with competitive routing ratios of \(1+6/(s-2)+4/s\) and \(1+6/(s-2)+6/s+4/(s^2-2s)+8/{s^2}\), respectively.

Research supported in part by NSERC and OGS.

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Correspondence to Frédérik Paradis .

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Bose, P., De Carufel, JL., Dujmović, V., Paradis, F. (2017). Local Routing in Spanners Based on WSPDs. In: Ellen, F., Kolokolova, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2017. Lecture Notes in Computer Science(), vol 10389. Springer, Cham. https://doi.org/10.1007/978-3-319-62127-2_18

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  • DOI: https://doi.org/10.1007/978-3-319-62127-2_18

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