Stable roommates spanner

We introduce a new geometric spanner whose construction is based on a generalization of the known Stable Roommates problem. The Stable Roommates Spanner combines the most desirable properties of geometric spanners: a natural definition, small degree, linear number of edges, strong (1+ε)-spanner for every ε>0, and an efficient construction algorithm. It is an improvement over the well-known Yao graph and Θ-graph and their variants. We show how to construct such a spanner for a set of points in the plane in O(n ^log10n) expected time. We introduce a variant of the Stable Roommates Spanner called the Stable Roommates Θ-Spanner which we can generalize to higher dimensions and construct more efficiently in O(n ^logdn) time. This variant possesses all the properties of the Stable Roommates Spanner except that it is no longer a strong spanner.