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(nlog10n) 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(nlogdn) time. This variant possesses all the properties of the Stable Roommates Spanner except that it is no longer a strong spanner.