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+225≈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+225 times the Euclidean distance between the vertices. We also give a lower bound on the spanning ratio of 12(115-17)≈3.798.

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Keywords Spanner, Spanning ratio, Stretch factor, Theta graph
Persistent URL
Journal Computational Geometry
Bose, P, Morin, P, Van Renssen, A. (André), & Verdonschot, S. (Sander). (2015). The θ5-graph is a spanner. Computational Geometry, 48(2), 108–119. doi:10.1016/j.comgeo.2014.08.005