L-Networks: A Topological Model for Regular 2D Interconnection Networks (original) (raw)

L-Networks: A Topological Model for Regular Two-Dimensional Interconnection Networks

2012

A complete family of Cayley graphs of degree four, denoted as L-networks, is considered in this paper. L-networks are two-dimensional mesh-based topologies with wraparound connections. L-networks constitute a graph-based model which englobe many previously proposed 2D interconnection networks. Some of them have been extensively used in the industry as the underlying topology for parallel and distributed computers of different scales. Tori, twisted and doubly twisted tori, toroidal diagonal meshes, chordal ...

A New Family of Cayley Graph Interconnection Networks of Constant Degree Four

IEEE Transactions on Parallel and Distributed Systems, 1996

We propose a new family of interconnection networks that are Cayley graphs with constant node degree 4. These graphs are regular, have logarithmic diameter and are maximally fault tolerant. We investigate different algebraic properties of these networks (including fault tolerance) and propose optimal routing algorithms. As far as we know, this is the first family of Cayley graphs of constant degree 4.

Lattice Graphs for High-Scale Interconnection Topologies

IEEE Transactions on Parallel and Distributed Systems, 2014

Torus networks of moderate degree have been widely used in the supercomputer industry. Tori are superb when used for executing applications that require near-neighbor communications. Nevertheless, they are not so good when dealing with global communications. Hence, typical 3D implementations have evolved to 5D networks, among other reasons, to reduce network distances. Most of these big systems are mixed-radix tori, which are not the best option for minimizing distances and efficiently using network resources. This paper is focused on improving the topological properties of this kind of networks.

Chordal Topologies for Interconnection Networks

2003

The class of dense circulant graphs of degree four with optimal distance-related properties is analyzed in this paper. An algebraic study of this class is done. Two geometric characterizations are given, one in the plane and other in the space. Both characterizations facilitate the analysis of their topological properties and corroborate their suitability for implementing interconnection networks for distributed and parallel computers. Also a distance-hereditary non-disjoint decomposition of these graphs into rings is computed. Besides its practical consequences, this decomposition allows us the presentation of these optimal circulant graphs as a particular evolution of the traditional ring topology.

A Class of Arc-Transitive Cayley Graphs as Models for Interconnection Networks

SIAM Journal on Discrete Mathematics, 2009

We study a class of Cayley graphs as models for interconnection networks. With focus on efficient communication we prove that for any graph in the class there exists a gossiping protocol which exhibits attractive features, and moreover we give an algorithm for constructing such a protocol. In particular, these hold for two important subclasses of graphs, namely, Cayley graphs admitting a complete rotation and Frobenius graphs of a certain type. For such Frobenius graphs, we obtain the minimum gossip time and give an optimal gossiping protocol under which messages are transmitted along shortest paths and each arc is used exactly once at each time step. Moreover, for such Frobenius graphs we construct an all-to-all routing which is a shortest path routing, arc-transitive, edge-and arc-uniform, and optimal for the edge-and arc-forwarding indices simultaneously.

Embeddings on Torus-Butterfly Interconnection Network

International Journal of Applied Information Systems, 2012

This paper discuss about embedding on the new interconnection network named Torus-Butterfly. Torus-Butterfly is the Cartesian product network that has constant degree and has smaller network cost than the other Cartesian product network. Torus-Butterfly network is a Cayley graph. From the properties of Cayley graphs which have Hamiltonian path, the linear array and 2D-Mesh can be embedded into this new Torus-Butterfly network with minimum dilation and expansion.

The optimization of chordal ring networks

1987

This paper deals with the design of multi-(micro)computer interconnection networks modelled by graphs. In particular we concentrate upon the optimization of a new family of such networks that turn out to be a generalization of the well-known Arden and Lee's chordal ring networks. This optimization problem leads to the search for certain 3-regular graphs with minimum diameter for a given order and/or maximum order for a given diameter. The use of a geometrical approach based on plane tessellations facilitates the solution of the problem.

Trivalent Cayley Graphs for Interconnection Networks

Information Processing Letters, 1995

We propose a new family of trivalent Cayley graphs with constant node degree 3 for design of interconnection networks. These graphs are shown to be regular, to have logarithmic diameter in the number of nodes, and to be maximally fault tolerant. We investigate different algebraic properties of these networks (including fault tolerance) and propose a simple routing algorithm.

CCTorus : A New Torus Topology for Interconnection Networks

The topology of interconnection networks plays a key role in the performance of all general purpose networking applications. Mesh, Torus, and Hypercube have been the most popular interconnection network topologies used in most of the digital communication systems. Among these topologies Torus is well suited in any general purpose networking application because of its simple network structure and high degree of symmetry. The performance of an interconnection network can be measured using various performance metrics as well as structural properties. Performance parameters that must be considered in designing an interconnection network are latency, throughput, cost, node degree, network diameters, and path diversity. Keeping these factors in mind, in this paper, we have proposed an interconnection network topology namely Centrally Connected Torus (CCTorus), which is the new version of classical Torus network. The aim is to achieve low latency, high throughput, minimum network diameter and better path diversity. In this paper the proposed topology is evaluated by using both theoretical analysis and simulations. Simulation results show that CCTorus has better scalability, and its average latency and average throughput is better than that of Mesh, XMesh, Torus, and XTorus by significant proportions respectively, particularly for larger size networks.

C2 Torus New Interconnection Network Topology Based on 2D Torus

American Journal of Networks and Communications

Mesh and Torus are most popular interconnection topologies based on 2D-mesh. Comparison between Mesh and Torus will be considered and new interconnection topology will be proposed to provide better performance. The C 2 Mesh is an enhanced mesh interconnected network. This paper enhances the Performance of torus network based on the theme of C 2 Mesh. Topological Properties of new network will be analyzed and implemented by simulation. The new routing Algorithm will be designed for new proposed network (C 2 Torus).