## Abstract

Given a set of points in the plane, we want to establish a connected spanning graph between these points, called connection network, that consists of several disjoint layers. Motivated by sensor networks, our goal is that each layer is connected, spanning, and plane. No edge in this connection network is too long in comparison to the length needed to obtain a spanning tree. We consider two different approaches. First we show an almost optimal centralized approach to extract two layers. Then we consider a distributed model in which each point can compute its adjacencies using only information about vertices at most a predefined distance away. We show a constant factor approximation with respect to the length of the longest edge in the graphs. In both cases the obtained layers are plane.

Original language | English |
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Pages (from-to) | 1-15 |

Number of pages | 15 |

Journal | Computational Geometry: Theory and Applications |

Volume | 82 |

DOIs | |

Publication status | Published - 2019 Sep |

## Keywords

- Bottleneck edge
- Geometric graphs
- Graph packing
- Minimum spanning tree
- Plane graphs

## ASJC Scopus subject areas

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