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)

On The Existence of Non-Diregular Digraphs of Order Two Less than the Moore Bound

A communication network can be modelled as a graph or a directed graph, where each processing element is represented by a vertex and the connection between two processing elements is represented by an edge (or, in case of directed connections, by an arc). When designing a communication network, there are several criteria to be considered. For example, we can require an overall balance of the system. Given that all the processing elements have the same status, the flow of information and exchange of data between processing elements will be on average faster if there is a similar number of interconnections coming in and going out of each processing element, that is, if there is a balance (or regularity) in the network. This means that the in-degree and out-degree of each vertex in a directed graph (digraph) must be regular. In this paper, we present the existence of digraphs which are not diregular (regular out-degree, but not regular in-degree) with the number of vertices two less than the unobtainable upper bound for most values of out-degree and diameter, the so-called Moore bound

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

Algebraic and Computer-based Methods in the Undirected Degree/diameter Problem - a Brief Survey

This paper discusses the most popular algebraic techniques and computational methods that have been used to construct large graphs with given degree and diameter

Properties and Algorithms of the KCube Graphs

The KCube interconnection topology was rst introduced in 2010. The KCube graph is a compound graph of a Kautz digraph and hypercubes. Compared with the at- tractive Kautz digraph and well known hypercube graph, the KCube graph could accommodate as many nodes as possible for a given indegree (and outdegree) and the diameter of interconnection networks. However, there are few algorithms designed for the KCube graph. In this thesis, we will concentrate on nding graph theoretical properties of the KCube graph and designing parallel algorithms that run on this network. We will explore several topological properties, such as bipartiteness, Hamiltonianicity, and symmetry property. These properties for the KCube graph are very useful to develop efficient algorithms on this network. We will then study the KCube network from the algorithmic point of view, and will give an improved routing algorithm. In addition, we will present two optimal broadcasting algorithms. They are fundamental algorithms to many applications. A literature review of the state of the art network designs in relation to the KCube network as well as some open problems in this field will also be given

The k-tuple twin domination in generalized de Bruijn and Kautz networks

AbstractGiven a digraph (network) G=(V,A), a vertex u in G is said to out-dominate itself and all vertices v such that the arc (u,v)∈A; similarly, u in-dominates both itself and all vertices w such that the arc (w,u)∈A. A set D of vertices of G is a k-tuple twin dominating set if every vertex of G is out-dominated and in-dominated by at least k vertices in D, respectively. The k-tuple twin domination problem is to determine a minimum k-tuple twin dominating set for a digraph. In this paper we investigate the k-tuple twin domination problem in generalized de Bruijn networks GB(n,d) and generalized Kautz GK(n,d) networks when d divides n. We provide construction methods for constructing minimum k-tuple twin dominating sets in these networks. These results generalize previous results given by Araki [T. Araki, The k-tuple twin domination in de Bruijn and Kautz digraphs, Discrete Mathematics 308 (2008) 6406–6413] for de Bruijn and Kautz networks

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

OTIS-Based Multi-Hop Multi-OPS Lightwave Networks

International audienceAdvances in optical technology, such as low loss Optical Passive Star couplers (OPS) and the possibility of building tunable optical transmitters and receivers have increased the interest for multiprocessor architectures based on lightwave networks because of the vast bandwidth available. Many research have been done at both technological and theoretical level. An essential effort has to be done in linking those results. In this paper we propose optical designs for two multi-OPS networks: the single-hop POPS network and the multi-hop stack-Kautz network; using the Optical Transpose Interconnecting System (OTIS) architecture, from the Optoelectronic Computing Group of UCSD. In order to achieve our result, we also provide the optical design of a generalization of the Kautz digraph, using OTIS