Abstract
In this paper we study the probabilistic properties of reliable networks of minimal total edge lengths. We study reliability in terms of k-edge-connectivity in graphs in d-dimensional space. We show this problem fits into Yukich’s framework for Euclidean functionals for arbitrary k, dimension d and distant-power gradient p, with p < d. With this framework several theorems on the convergence of optimal solutions follow. We apply Yukich’s framework for functionals so that we can use partitioning algorithms that rapidly compute near-optimal solutions on typical examples. These results are then extended to optimal k-edge-connected power assignment graphs, where we assign power to vertices and charge per vertex. The network can be modelled as a wireless network.
| Original language | English |
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| Pages | 105-108 |
| Number of pages | 4 |
| Publication status | Published - 6 Jun 2017 |
| Event | 15th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2017 - Cologne, Germany Duration: 6 Jun 2017 → 8 Jun 2017 Conference number: 15 http://ctw.uni-koeln.de/ |
Conference
| Conference | 15th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2017 |
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| Abbreviated title | CTW |
| Country | Germany |
| City | Cologne |
| Period | 6/06/17 → 8/06/17 |
| Internet address |
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Cite this
Reijnders, V. M. J. J., & Manthey, B. (2017). Probabilistic Properties of Highly Connected Random Geometric Graphs. 105-108. Abstract from 15th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2017, Cologne, Germany.