A neural optimizer for hypercube embedding

International Journal of Parallel Programming, 1989

The hypercube embedding problem, a restricted version of the general mapping problem, is the problem of mapping a set of communicating processes to a hypercube multiprocessor. The goal is to find a mapping that minimizes the length of the paths between communicating processes. Unfortunately the hypercube embedding problem has been shown to be NP-hard. Thus many heuristics have been proposed

Mathematical and Computer Modelling, 1988

One important aspect of efficient use of a hypercube computer to solve a given problem is the assignment of subtasks to processors in such a way that the communication overhead is low. The subtasks and their inter-communication requirements can be modeled by a ...

[1991] Proceedings. The Fifth International Parallel Processing Symposium

The hypercube has emerged as one of the most e ective and popular architecture for parallel machines and several hypercube based machines (e.g; Intel IPSc and NCUBE) are commercially available. Hypercube popularity may be attributed to its regular structure and its rich interconnection topology 17]. Despite its versatility, hypercube topology requires that the number of nodes must be a power of 2. In order to alleviate this shortcoming, several`incomplete' hypercube-like architectures have been proposed. Katse proposed in 13] an n-node Incomplete Hypercube by taking nodes 0 through n ? 1 of a complete hypercube. He showed that broadcasting and nodeto-node communication algorithms for incomplete hypercubes are similar to ones of a complete hypercube. Tzeng et. al. 18] investigated a restricted version of the Katse 's de nition by considering only those nnode incomplete hypercubes, where n = 2 l + 2 m ; l > m. They investigated the capability of this architecture to simulate binary trees and two dimensional meshes. In 4, 7], we de ned a generalization of incomplete hypercubes, called Composite Hypercubes. Composite hypercubes are not restricted to the rst n nodes of a com

Parallel Computing, 1989

Boltzmann machines offer an exciting approach to connectionist networks. Salient features of these networks are their distributed internal representations and their use of massive parallelism. This paper reviews some of the achievements in the research on Boltzmann machines and discusses in particular two different fields of application, viz. (i) solving combinatorial optimization problems and (ii) carrying out learning tasks. Some open problems are also touched upon.

The Journal of Supercomputing, 1989

Several approaches to finding the connected components of a graph on a hypercube multicomputer are proposed and analyzed. The results of experiments conducted on an NCUBE hypercube are also presented. The experimental results support the analysis.

One important aspect of efficient use of a hypercube computer to solve a given problem is the assignment of subtasks to processors in such a way that the communication overhead is low. The subtasks and their inter-communication requirements can be modeled by a graph, and the assignment of subtasks to processors viewed as an embedding of the task graph into the graph of the hypercube network. We survey the known results concerning such embeddings, including expansion/dilation tradeoffs for general graphs, embeddings of meshes and trees, packings of multiple copies of a graph, the complexity of finding good embeddings, and critical graphs which are minimal with respect to some property. In addition, we describe several open problems. . the hypercube is used to simulate a network with graph G the nodes of G must be mapped to the nodes of Q n , and, in order to keep communication overhead down, adjacent nodes of G should map to adjacent nodes of Q n insofar as possible. In designing (or adapting) an algorithm that performs a task T on the hypercube network, T is modeled with a "task graph", G T , in which the nodes represent subtasks and the edges represent communication requirements between the corresponding subtasks. Once again, the efficiency of the implementation depends strongly on the nature of the mapping into Q n . To keep communication overhead low, the nodes of G T must be mapped to the nodes of Q n so that pairs of adjacent nodes of G T map to pairs of adjacent nodes of Q n .

Information Processing Letters, 1987

The problem of embedding a graph into a fixed-size hypercube is shown to be NP-complete. This work complements recent work of the present authors showing that deciding whether a graph is embeddable into any size hypercube is NP-complete as well. The reduction is from 3-partition.

Journal of Systems Architecture, 2000

Topology and routing algorithm are among the most important factors that greatly in¯uence network performance. This paper assesses the interaction of these factors on two related but distinct types of multicomputer networks, the hypercube and hypermesh. This study shows that the routing algorithm can have a great in¯uence on deciding the outcome of any comparison between competing network topologies. The results reveal that deterministic routing favours the hypermesh due to its smaller diameter which reduces considerably message blocking compared to the hypercube. However, adaptive routing favours the hypercube as it can bene®t from its multiple paths to overcome the degrading eects of its high diameter.

International Journal of Computer Applications, 2015

This paper is concerned with routing of data in an embedded hypercube interconnection using the approach based on neural net architecture. To present a framework of the interconnection network consist number of nodes and number of connections. In this paper we first show that n dimensional hypercube can be embedded in layer neural layer network such that for any node of hypercube, its neighboring nodes of other layer are evenly partition into layers where each layer shares a manipulating or resulting data of different layers. Under this embedding network to fixed target and varying data input to produce output of the two incidence matrix of kary n-cube network to embedded in architecture.

Journal of Parallel and Distributed Computing, 1993

When each G j is a complete binary tree or a leap tree of 2 k-1 nodes, we describe an embedding achieving a dilation of 2 and a load of 5 and 6, respectively. For the cases when each G j is a linear array or a 2-dimensional mesh of 2 k nodes, we describe embeddings that achieve a dilation of 1 and an optimal load of 2 and 4, respectively. Using these embeddings, we also show that Tl complete binary trees, T2 leap trees, T3 linear arrays, and T 4 meshes can simultaneously be embedded into H with 1 constant dilation and load, L Tj :$ k.