New Class Of Interconnection Networks Research Articles

An analysis of the topological properties of the interlaced bypass torus (iBT) networks

We analyze a new class of interconnection networks that are constructed by interlacing bypass rings to the torus network (iBT network). We establish the minimum conditions a bypass scheme needs to satisfy for generating a qualified iBT network and then we develop a recursive algorithm to calculate all of the qualified bypass schemes for a given network size and node degree. Our algorithm enables us to discover a class of the most efficient networks with up to 1 million nodes when considering the diameters of various iBT networks as a function of the bypass schemes. These analyses help achieve maximal performance improvement by the best bypass schemes.

The automorphism group of the alternating group graph

Let A n be the alternating group of degree n with n ≥ 3 . Set S = { ( 1 2 i ) , ( 1 i 2 ) ∣ 3 ≤ i ≤ n } . The alternating group graph, denoted by A G n , is defined as the Cayley graph on A n with respect to S . Jwo et al. (1993) [J.-S. Jwo, S. Lakshmivarahan, S.K. Dhall, A new class of interconnection networks based on the alternating group, Networks 23 (1993) 315–326] introduced the alternating group graph A G n as an interconnection network topology for computing systems, and they proved that A G n is arc-transitive. In this work, it is shown that the full automorphism group of A G n is the semi-direct product R ( A n ) ⋊ Aut ( A n , S ) , where R ( A n ) is the right regular representation of A n and Aut ( A n , S ) = { α ∈ Aut ( A n ) ∣ S α = S } ≅ S n − 2 × S 2 . It follows from this result that A G n is arc-transitive but not 2-arc-transitive.

Properties of a hierarchical network based on the star graph

This paper introduces a new class of interconnection networks named star-pyramid. An n-level star-pyramid is formed by piling up star graphs of dimensions 1 to n in a hierarchy, connecting any node in each i-dimensional star, 1

Dual of a Complete Graph as an Interconnection Network

A new class of interconnection networks, the hypernetworks, has been proposed recently. Hypernetworks are characterized by hypergraphs. Compared with point-to-point networks, they allow for increased resource-sharing and communication bandwidth utilization, and they are especially suitable for optical interconnects. In this paper, we propose a scheme for deriving new hypernetworks using hypergraph duals. As an example, we investigate the dual, K*n, of the n-vertex complete graph Kn and show that it has many desirable properties. We also present a set of fundamental data communication algorithms for K*n. Our results indicate that the K*n hypernetwork is a useful and promising interconnection structure for high-performance parallel and distributed computing systems.

Incrementally extensible folded hypercube graphs

In this paper, we propose the incrementally extensible folded hypercube (IEFH) graph as a new class of interconnection networks for an arbitrary number of nodes. We show that this system is optimal fault tolerant and almost regular (i.e., the difference between the maximum and the minimum degree of nodes is at most one). The diameter of this topology is half of that of the incomplete hypercube (IH), the supercube, or the IEH graph. We also devise a simple routing algorithm for the IEFH graph. Finally, we embed cycles and complete binary trees into this graph optimally.

Macro-star networks: efficient low-degree alternatives to star graphs

We propose a new class of interconnection networks, called macro-star networks, which belong to the class of Cayley graphs and use the star graph as a basic building module. A macro-star network can have node degree that is considerably smaller than that of a star graph of the same size, and diameter that is sublogarithmic and asymptotically within a factor of 1.25 from a universal lower bound (given its node degree). We show that algorithms developed for star graphs can be emulated on suitably constructed macro-stars with asymptotically optimal slowdown. This enables us to obtain through emulation a variety of efficient algorithms for the macro-star network, thus proving its versatility. Basic communication tasks, such as the multimode broadcast and the total exchange, can be executed in macro-star networks in asymptotically optimal time under both the single-port and the all-port communication models. Moreover, no interconnection network with similar node degree can perform these communication tasks in time that is better by more than a constant factor than that required in a macro-star network. We show that macro-star networks can embed trees, meshes, hypercubes, as well as star, bubble-sort, and complete transposition graphs with constant dilation. We introduce several variants of the macro-star network that provide more flexibility in scaling up the number of nodes. We also discuss implementation issues and compare the new topology with the star graph and other popular topologies.

DCC linear congruential graphs: a new class of interconnection networks

Let n be an integer and F={f/sub 1/:1/spl les/i/spl les/t for some integer t} be a finite set of linear functions. We define a linear congruential graph G(F, n) as a graph on the vertex set V={0, 1, ..., n-1}, in which any x/spl isin/V is adjacent to f/sub i/(x) mod n, 1/spl les/i/spl les/t. For a linear function g, and a subset V/sub 1/ of V we define a linear congruential graph G(F, n, g,V/sub 1/) as a graph on vertex set V, in which any x/spl isin/V is adjacent to f/sub i/(x) mod n, 1/spl les/i/spl les/t, and any x/spl isin/V/sub 1/ is also adjacent to g(x) mod n. These graphs generalize several well known families of graphs, e.g. the de Bruijn graphs. We give a family of linear functions, called DCC linear functions, that generate regular, highly connected graphs which are of substantially larger order than de Bruijn graphs of the same degree and diameter. Some theoretical and empirical properties of these graphs are given and their structural properties are studied.

ANALYSIS OF A CLASS OF NETWORKS BASED ON CUBIC STAR GRAPHS

A new class of interconnection networks based on a family of graphs, called cubic graphs are introduced. These latter graphs arise as Cayley graphs of certain subgroups of the symmetric group. It turns out that these Cayley graphs are a hybrid between the binary hypercube and the star graph, and hence are called cubic star graphs, and are denoted by CS(m, n), m≥1 and n≥1. CS(m, n) inherits several of the properties of the hypercube and the star graph. In this paper, we present an analysis of the symmetric and topological properties. In particular, it is shown that CS(m, n) is edge transitive and hence maximally fault tolerant. We give an algorithm for finding the shortest path and provide an enumeration of the node disjoint paths. Optimal algorithms for single source and all-source broadcasting (also called gossiping) are derived. It is shown that CS(m, n) is Hamiltonian and interesting embeddings of several cycles, grids, and binary trees are derived. The paper concludes with a comparison of CS(m, n) with the binary hypercube and the star graph.

An Efficient Class of Interconnection Networks for Parallel Computations

A new class of interconnection networks is presented for interconnecting the processors of general purpose massively parallel computers. This new class of interconnection networks, recursively connected networks (RCN), is contructed by methodically connecting together a number of basic networks, referred to as atoms, through the recursive application of a complete graph compound. A specific instance of this class, RCN-CUBE, where the basic atom is a binary hypercube, is shown to have desirable network properties such as small diameter, small degree, high bandwidth and optimal connectivity; and these compare favorably to those of other related networks

A class of recursive interconnection networks: architectural characteristics and hardware cost

We propose and analyze a new class of interconnection networks, RCC, for interconnecting the processors of a general purpose parallel computer system. The RCC is constructed incrementally through the recursive application of a complete graph compound. The RCC integrate positive features of both complete networks and a given basic network. This paper presents the principles of constructing RCC and analyzes its architectural characteristics, its message routing capability, and its hardware cost. A specific instance of this class, RCC-CUBE, is shown to have desirable network properties such as small diameter, small degree, high density, high bandwidth, and high fault tolerance and is shown that they compare favorably to those of the hypercube, the 2-D, mesh, and the folded hypercube. Moreover, RCC-CUBE is shown to emulate the hypercube in constant time under any message distribution. The hardware cost and physical time performance are estimated under some packaging constraints for RCC-CUBE and compared to those of the hypercube, the folded hypercube, and the 2-D mesh demonstrating an overall cost effectiveness for RCC-CUBE. Hence, the RCC-CUBE appears to be a good candidate for next generation massively parallel computer systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A new class of interconnection networks based on the alternating group

AbstractThis paper introduces a new class of interconnection scheme based on the Cayley graph of the alternating group. It is shown that this class of graphs are edge symmetric and 2‐transitive. We then describe an algorithm for (a) packet routing based on the shortest path analysis, (b) finding a Hamiltonian cycle, (c) ranking and unranking along the chosen Hamiltonian cycle, (d) unit expansion and dilation three embedding of a class of two‐dimensional grids, (e) unit dilation embedding of a variety of cycles, and (f) algorithm for broadcasting messages. The paper concludes with a short analysis of contention resulting from a typical communication scheme. Although this class of graphs does not possess many of the symmetry properties of the binary hypercube, with respect to the one source broadcasting, these graphs perform better than does a hypercube, and with respect to the contention problem, these graphs perform better than do the star graphs and are close to the hypercube. © 1993 by John Wiley &amp; Sons, Inc.

A new class of fault-tolerant static interconnection networks

The authors present a new class of interconnection networks using combinatorial block designs. These networks are highly structured and have strong fault-tolerant properties. They also have a free parameter that allows tradeoffs to be made between performance and cost in a fairly continuous way.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>