L-Networks: A Topological Model for Regular Two-Dimensional Interconnection Networks (original) (raw)

L-Networks: A Topological Model for Regular 2D Interconnection Networks

IEEE Transactions on Computers, 2000

A complete family of Cayley graphs of degree four, denoted as L-networks, is considered in this paper. Lnetworks 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 rings, and circulant graphs are, among others, members of the L-network family. Therefore, many results obtained in previous studies on these networks can be deduced from the general framework presented in this work. In addition, the network model presented in this work allows for new results on the domain of low-degree interconnection networks. Particularly, closed expressions for the graph distance properties have been derived and an optimal routing algorithm of constant complexity is provided. Since symmetry has a big impact on network performance, we have also identified which L-networks are symmetric by studying their group of automorphisms. Finally, a very simple model that predicts the performance of L-networks is also presented. Such model has been contrasted with empirical evaluation. Lemma 4. [23] Let Γ be a finite Abelian group, A = {±a, ±b} ⊆ Γ and consider Cay(Γ; A). Then, there exists M ∈ Z 2×2 such that Cay(Γ; A) ∼ = L(M ).

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 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.

Hierarchical Tori Connected Mesh Network

Lecture Notes in Computer Science, 2013

Hierarchical interconnection networks provide high performance at low cost by exploring the locality that exists in the communication patterns of massively parallel computers. A Hierarchical Tori connected Mesh Network (HTM) is a 2D-torus network of multiple basic modules, in which the basic modules are 3D-mesh networks that are hierarchically interconnected for higher-level networks. This paper addresses the architectural details of the HTM and explores aspects such as degree, diameter, cost, average distance, arc connectivity, bisection width, and wiring complexity. We also present a deadlock-free routing algorithm for the HTM using two virtual channels and evaluate the network's dynamic communication performance using the proposed routing algorithm under uniform traffic and bit-flip traffic patterns. We evaluate the dynamic communication performance of HTM, H3DM, mesh, and torus networks by computer simulation. It is shown that the HTM possesses several attractive features, including constant node degree, small diameter, low cost, small average distance, moderate (neither too low, nor too high) bisection width, small wiring complexity, and high throughput per link and very low zero load latency, which provide better dynamic communication performance than that of H3DM, mesh, and torus 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).

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.

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.

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.

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.