The θ 5-Graph is a Spanner

نویسندگان

  • Prosenjit Bose
  • Pat Morin
  • André van Renssen
  • Sander Verdonschot
چکیده

Given a set of points in the plane, we show that the θ-graph with 5 cones is a geometric spanner with spanning ratio at most √ 50 + 22 √ 5 ≈ 9.960. This is the first constant upper bound on the spanning ratio of this graph. The upper bound uses a constructive argument that gives a (possibly self-intersecting) path between any two vertices, of length at most √ 50 + 22 √ 5 times the Euclidean distance between the vertices. We also give a lower bound on the spanning ratio of 1 2 (11 √ 5− 17) ≈ 3.798.

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تاریخ انتشار 2013