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Reports Year : 2005

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

Anthony Busson
Guillaume Chelius
  • Function : Author
Eric Fleury
  • Function : Author

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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Other [cs.OH]
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Dates and versions

inria-00070502 , version 1 (19-05-2006)

Identifiers

  • HAL Id : inria-00070502 , version 1

Cite

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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