On the stretch factor of the theta-4 graph

Authors:
Luis Barba;Prosenjit Bose;Jean-Lou De Carufel;André van Renssen;Sander Verdonschot
Affiliations:
School of Computer Science, Carleton University, Ottawa, Canada,Département d'Informatique, Université Libre de Bruxelles, Brussels, Belgium;School of Computer Science, Carleton University, Ottawa, Canada;School of Computer Science, Carleton University, Ottawa, Canada;School of Computer Science, Carleton University, Ottawa, Canada;School of Computer Science, Carleton University, Ottawa, Canada
Venue:
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Year:
2013

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Abstract

In this paper we show that the θ-graph with 4 cones has constant stretch factor, i.e., there is a path between any pair of vertices in this graph whose length is at most a constant times the Euclidean distance between that pair of vertices. This is the last θ-graph for which it was not known whether its stretch factor was bounded.