On a family of strong geometric spanners that admit local routing strategies

Prosenjit Bose, Paz Carmi, Mathieu Couture, Michiel Smid, Daming Xu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We introduce a family of directed geometric graphs, whose vertices are points in Rd. The graphs Gλθ in this family depend on two real parameters λ and θ. For 12<λ<1 and π3<θ<π2, the graph Gλθ is a strong t-spanner for t=1(1-λ)cosθ. That is, for any two vertices p and q, Gλθ contains a path from p to q of length at most t times the Euclidean distance |pq|, and all edges on this path have length at most |pq|. The out-degree of any node in the graph Gλθ is O(1/πd- 1), where π=min(θ,arccos12λ). We show that routing on Gλθ can be achieved locally. Finally, we show that all strong t-spanners are also t-spanners of the unit-disk graph.

Original languageEnglish
Pages (from-to)319-328
Number of pages10
JournalComputational Geometry: Theory and Applications
Issue number6-7
StatePublished - 1 Aug 2011
Externally publishedYes


  • Geometric spanner
  • Local routing algorithms
  • Yao graph

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics


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