# The Eulerian stretch of a digraph and the ending guarantee of a convergence routing

1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
3 RESEDAS - Software Tools for Telecommunications and Distributed Systems
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : In this paper, we focus on convergence packet routing techniques in a network, obtained from an Eulerian routing in the digraph modeling the target network. Given an Eulerian circuit $\cal C$ in a digraph $G$, we consider the maximal number $diamW_{\cal C}$ of arcs that a packet has to follow on $\cal C$ from its origin to its destination (we talk about the {\em ending guarantee} of the routing). We consider the {\em Eulerian diameter of $G$} as defined by ${\cal E}(G)=\min\limits_{{\cal C}? Eul(G)} diamW_{\cal C}$, where $Eul(G)$ is the set of all the Eulerian circuits in $G$. After giving a preliminary result about the complexity of finding ${\cal E}(G)$ for any digraph $G$, we give some lower and upper bounds of this parameter. We conclude by giving some families of digraphs having good Eulerian diameter.
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https://hal.inria.fr/inria-00099331
Contributor : Publications Loria <>
Submitted on : Tuesday, September 26, 2006 - 8:52:59 AM
Last modification on : Friday, February 26, 2021 - 3:28:07 PM

### Identifiers

• HAL Id : inria-00099331, version 1

### Citation

Dominique Barth, Pascal Berthomé, Johanne Cohen. The Eulerian stretch of a digraph and the ending guarantee of a convergence routing. [Intern report] A00-R-400 || barth00a, 2000, 22 p. ⟨inria-00099331⟩

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