Local Routing in Spanners Based on WSPDs

  • Prosenjit Bose
  • Jean-Lou De Carufel
  • Vida Dujmović
  • Frédérik ParadisEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10389)


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.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Prosenjit Bose
    • 1
  • Jean-Lou De Carufel
    • 2
  • Vida Dujmović
    • 2
  • Frédérik Paradis
    • 2
    Email author
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.School of Electrical Engineering and Computer ScienceUniversity of OttawaOttawaCanada

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