## Abstract

We introduce a family of directed geometric graphs, whose vertices are points in ^{Rd}. The graphs Gλθ in this family depend on two real parameters λ and θ. For 12<λ<1 and π3<θ<π2, the graph Gλθ is a strong t-spanner for t=1(1-λ)cosθ. That is, for any two vertices p and q, Gλθ contains a path from p to q of length at most t times the Euclidean distance |pq|, and all edges on this path have length at most |pq|. The out-degree of any node in the graph Gλθ is O(1/πd- ^{1}), where π=min(θ,arccos12λ). We show that routing on Gλθ can be achieved locally. Finally, we show that all strong t-spanners are also t-spanners of the unit-disk graph.

Original language | English |
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Pages (from-to) | 319-328 |

Number of pages | 10 |

Journal | Computational Geometry: Theory and Applications |

Volume | 44 |

Issue number | 6-7 |

DOIs | |

State | Published - 1 Aug 2011 |

Externally published | Yes |

## Keywords

- Geometric spanner
- Local routing algorithms
- Yao graph

## ASJC Scopus subject areas

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