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
