On hardware for generating routes in Kautz digraphs

In this paper we present a hardware implementation of an algorithm for generating node disjoint routes in a Kautz network. Kautz networks are based on a family of digraphs described by W.H. Kautz[Kautz 68]. A Kautz network with in-degree and out-degree d has N = dk + dk¿1 nodes (for any cardinals d, k>0). The diameter is at most k, the degree is fixed and independent of the network size. Moreover, it is fault-tolerant, the connectivity is d and the mapping of standard computation graphs such as a linear array, a ring and a tree on a Kautz network is straightforward.\ud The network has a simple routing mechanism, even when nodes or links are faulty. Imase et al. [Imase 86] showed the existence of d node disjoint paths between any pair of vertices. In Smit et al. [Smit 91] an algorithm is described that generates d node disjoint routes between two arbitrary nodes in the network. In this paper we present a simple and fast hardware implementation of this algorithm. It can be realized with standard components (Field Programmable Gate Arrays)

Notes on the connectivity of Cayley coset digraphs

Hamidoune's connectivity results for hierarchical Cayley digraphs are extended to Cayley coset digraphs and thus to arbitrary vertex transitive digraphs. It is shown that if a Cayley coset digraph can be hierarchically decomposed in a certain way, then it is optimally vertex connected. The results are obtained by extending the methods used by Hamidoune. They are used to show that cycle-prefix graphs are optimally vertex connected. This implies that cycle-prefix graphs have good fault tolerance properties.Comment: 15 page

A Switch Architecture for Real-Time Multimedia Communications

In this paper we present a switch that can be used to transfer multimedia type of trafJic. The switch provides a guaranteed throughput and a bounded latency. We focus on the design of a prototype Switching Element using the new technology opportunities being offered today. The architecture meets the multimedia requirements but still has a low complexity and needs a minimum amount of hardware. A main item of this paper will be the background of the architectural design decisions made. These include the interconnection topology, buffer organization, routing and scheduling. The implementation of the switching fabric with FPGAs, allows us to experiment with switching mode, routing strategy and scheduling policy in a multimedia environment. The witching elements are interconnected in a Kautz topology. Kautz graphs have interesting properties such as: a small diametec the degree is independent of the network size, the network is fault-tolerant and has a simple routing algorithm

Topologies for Optical Interconnection Networks Based on the Optical Transpose Interconnection System

International audienceMany results exist in the literature describing technological and theoretical advances in optical network topologies and design. However, an essential effort has yet to be done in linking those results together. In this paper, we propose a step in this direction, by giving optical layouts for several graph-theoretical topologies studied in the literature, using the Optical Transpose Interconnection System (OTIS) architecture. These topologies include the family of Partitioned Optical Passive Star (POPS) and stack-Kautz networks as well as a generalization of the Kautz and de Bruijn digraphs

Topologies for Optical Interconnection Networks Based on the Optical Transpose Interconnection System

International audienceMany results exist in the literature describing technological and theoretical advances in optical network topologies and design. However, an essential effort has yet to be done in linking those results together. In this paper, we propose a step in this direction, by giving optical layouts for several graph-theoretical topologies studied in the literature, using the Optical Transpose Interconnection System (OTIS) architecture. These topologies include the family of Partitioned Optical Passive Star (POPS) and stack-Kautz networks as well as a generalization of the Kautz and de Bruijn digraphs