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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 C in a digraph C, we deal with the maximal number diamWC of arcs that a packet has to follow on C from its origin to its destination (we talk about the ending guarantee of the routing). We consider the Eulerian diameter of C as defined by E(C) = mm C ∈ Eul(G) diamWc, where E(G) is the set of all the Eulerian circuits in C. After giving a preliminary result about the complexity of finding ((C) 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. [ABSTRACT FROM AUTHOR]

In this paper we study the square grid area required for laying out H[sub l], the Boolean hypercube of N=2[sup l] vertices. It is shown that this area is [formula]. We describe a layout which occupies this much area and prove that no layout of less area exists. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of constructing a multicast tree in star interconnection networks under the single-port communication model. Unlike previous schemes for constructing space-efficient multicast trees, we adopt the completion time of each multicast as the objective function to be minimized. In particular, we study a special case of the problem in which all destination vertices are immediate neighbors of the source vertex, and propose a multicast scheme of [formula] time units for the star graph of dimension n. [ABSTRACT FROM AUTHOR]