# From euclidian to hop distance in multi-hop radio networks: a discrete approach

1 ARES - Architectures of networks of services
Inria Grenoble - Rhône-Alpes, CITI - CITI Centre of Innovation in Telecommunications and Integration of services
Abstract : In this article, we formalize the relation $\mathbbP(N_d=n)$ between the hop distance and the euclidian distance in 1-dimensional and 2-dimensional discrete networks. We provide closed formulas for the mean hop distance between two arbitrary nodes depending on their euclidian distance in both discrete and continuous networks. More generally, we also formally prove that results computed in discrete networks induce boundaries in continuous ones. Moreover, as the step of the discrete network is decreased, discrete results converge towards continuous ones. This phenomena justifies the methodology consisting in considering discrete networks to study properties that are hardly tractable in continuous networks.
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Cited literature [3 references]

https://hal.inria.fr/inria-00070502
Contributor : Rapport de Recherche Inria <>
Submitted on : Friday, May 19, 2006 - 8:41:03 PM
Last modification on : Wednesday, July 8, 2020 - 12:42:10 PM
Long-term archiving on: : Monday, September 17, 2012 - 4:00:33 PM

### Identifiers

• HAL Id : inria-00070502, version 1

### Citation

Anthony Busson, Guillaume Chelius, Eric Fleury. From euclidian to hop distance in multi-hop radio networks: a discrete approach. RR-5505, INRIA. 2005, pp.29. ⟨inria-00070502⟩

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