## Abstract

Given a set S of points in the plane representing wireless devices, each point equipped with a directional antenna of radius r and aperture angle α ≥ 180°, our goal is to find orientations and a minimum r for these antennas such that the induced communication graph is strongly connected. We show that r = √ 3 suffices to establish strong connectivity, assuming that the longest edge in the Euclidean minimum spanning tree for S is 1. This result is optimal in the sense that r = √ 3 is necessary in the worst-case for α ∈ [180°; 240°). In contrast, r = 2 is sometimes necessary when α < 180°.

Original language | English |
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Publication status | Published - 2011 |

Event | 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011 - Toronto, ON, Canada Duration: 2011 Aug 10 → 2011 Aug 12 |

### Other

Other | 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011 |
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Country/Territory | Canada |

City | Toronto, ON |

Period | 11/8/10 → 11/8/12 |

## ASJC Scopus subject areas

- Computational Mathematics
- Geometry and Topology