Hyper Petersen network: yet another hypercube-like topology

Abstract

We propose and analyze a new hypercube-like topology, called the hyper Petersen (HP) network, which is constructed from the Cartesian product of a binary hypercube and the well-known Petersen graph. The properties of HP topology include regularity, high degree of symmetry and connectivity, and small diameter. For ezample, an n-dimensional HP network with N = 1.25 * 2" nodes is a regular graph having degree 6 = n, node-connectivity n = n, and diameter d = n -1, whereas a binary hypercube graph with the same diameter covers only 2"-l nodes, each of degree ( nl). Thus the HP topology covers t.5 times extra nodes at the cost of increasing the degree by one. Furthermore with the same degree and .conneetivity (i.e. 6 = n = n), the diameter of the HP network is one less than that of a hypercube, yet having 1.25 times higher packing density. This paper also dascusses embedding of various other topologies such as meshes, trees, twisted hypercubes on the HP topology, thereby emphasizing its rich interconnection structure with simple routing scheme for message communication. A ring of odd length can be embedded i n an HP network, which is a limitation of a binary hypercube. IntroductionOne of the important aspects of a message-passing parallel computer is its interconnection network topology which is most often represented by an undirected graph such that each node represents a processor and an edge is a full-du lex communication link between two processors [4,12f. Several network topologies have been proposed, e.g. trees, meshes, shuffle exchange, hypercubes, cube connected cycles 211, pyrayids [25], works 10 1 4 , star and pancakes [2/, de Bruijn networks 1231, and 80 on. Among these networks, the hypercube has received the maximum attention because of its rich interconnection structuresuch as symmetry, high node-hypernet [20, Stirling networks [ I 2 , recursive nett This rescar& in supported by Tczar Advanced Rcrtarch Progmm grant under TARP Award No. 003594003. For commenta or reprints, please contact dasOpondm.o5ci.uut.edu or at (817) 5684256. TX 76203-3886 connectivity, logarithmic degree and diameterand because several commercial parallel machines (e.g. Intel iPSC [24], NCUBE [lq, Connection machine [19]) Definitions and TerminologyAn interconnection network is usually modeled as an undirected graph G = (V, E where V is the nodetheoretic terminofogy [8].The degree, deg U), of a node U is the number of its tion cost. If 6 = deg(u), for 1 5 U 5 IVl = N, then G diameter is re a uced without increasing node degrees, set and E the ed e-set. We wi t use standard graphcommunication lii L , which is a measure of its connec-270 0-8186-2772-7/92 $3.00 0 1992 IEEE

One-to-One Embedding between Hyper Petersen and Petersen-Torus Networks

“…The nature of Hyper Petersen is very similar to that of Hypercube, and the number of nodes for Hyper Petersen is more than 1.25 times of Hypercube on condition that it has similar diameter and degree [6].…”

“…j-dimension HP consists of 10×2 j-3 nodes and 5j×2 j-3 edges and is indicated in HP j =(V hp , E hp ). A set of peaks is composed of two tuples and defined as follows [6]:…”

Comparative Study of Product Networks

“…This set includes the following networks: hypercube, mesh, star graph [1], deBruijn network [19], product-shuffle network [18], hyper-Petersen network [4], mesh-connected-trees [8], hyper-deBruijn network [9], dBCube network [3], star-cube network [6], and hyperstar network [5]. We base our comparison on some of the most widely used criteria including network scalability, cost of broadcasting, embedding of other important topologies, cost/performance ratio, area of VLSI layout, and basic attributes of degree, diameter, and total number of links.…”

“…This framework covers a wide range of well-known topologies such as hypercubes, k-ary n-cubes, meshes, and generalized hypercubes. Based on this framework several other examples of product networks have been proposed and studied including hyperPetersen network [4], folded Petersen cube network [16], mesh-connected-trees [8], product-shuffle network [18], hyper-deBruijn network [9], star-cube network [6], and hyperstar network [5]. Rosenberg [18] studies the product-shuffle network (product of deBruijn graphs) and obtains embedding, network emulation, and VLSI layout results for this product network.…”

“…In [4], Das and Banerjee studied the graph product of the hypercube and the Petersen graph. The hyper-Petersen covers 25% extra nodes using the same number of links as the hypercube.…”