THE EULERIAN STRETCH OF A NETWORK TOPOLOGY AND THE ENDING GUARANTEE OF A CONVERGENCE ROUTING

Abstract

In this paper, we focus on convergence packet routing techniques in an all-optical network, obtained from an Eulerian routing in the digraph modeling the target network. Given an Eulerian circuit [Formula: see text] in a digraph G, we deal with the maximal number [Formula: see text] of arcs that a packet has to follow on [Formula: see text] from its origin to its destination (we talk about the ending guarantee of the routing). We consider the Eulerian diameter of G as defined by [Formula: see text], where Eul(G) is the set of all the Eulerian circuits in G. After giving a preliminary result about the complexity of finding ℰ(G) for any digraph G, we give some lower and upper bounds of this parameter. The main part of the paper is devoted to the description of a combinatorial design of various network topologies having good Eulerian diameters.