## Abstract

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 ^{log10}n) 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 ^{logd}n) time. This variant possesses all the properties of the Stable Roommates Spanner except that it is no longer a strong spanner.

Original language | English |
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Pages (from-to) | 120-130 |

Number of pages | 11 |

Journal | Computational Geometry: Theory and Applications |

Volume | 46 |

Issue number | 2 |

DOIs | |

State | Published - 1 Feb 2013 |

## Keywords

- Geometric spanners
- Stable Roommates
- Yao graph
- Θ-graph

## ASJC Scopus subject areas

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics