Finding and Displaying the Shortest Paths in Hyper-Rings (original) (raw)

DVcube: A novel compound architecture of disc-ring graph and hypercube-like graph

2013

In this paper, we first introduce a family of interconnection network topologies, named disc-ring graphs. Disc-ring graphs possess many desirable topological properties in building parallel machines, such as fixed degree, small diameter, Hamiltonian decomposition, etc. We first examine the topological properties of disc-ring graphs and give an efficient routing algorithm for disc-ring graphs. We then bring forward a novel interconnection network of DQcube, which is a compound graph of disc-ring graph and hypercube. That is, it uses the hypercube as a unit cluster and connects many such clusters by means of a disc-ring graph at the cost that only one additional link is added to any node in each hypercube. The topological benefits of both basic graphs are preserved in the compound network. It utilizes the topological properties of hypercube to conveniently embed parallel algorithms into each cluster and the short diameter of disc-ring graph to support an efficient inter-cluster communication. The proposed methodologies for DQcube are further applied to many other compound graphs of disc-ring graph and hypercube-like graphs, including locally twisted cube, twisted cube, crossed cube, and Möbius cube, with diameter being a half of that of hypercube. We also give and analyze an efficient routing algorithm for the proposed compound networks in this article.

KH-map: A new way of representing the hypercube structure

Journal of Systems Architecture, 1998

The hypercube structure is an attractive and powerful topology for interconnecting processing elements in a multiprocessor system since it allows simple deadlock-free routing and broadcasting. In a hypercube architecture, one has to visualize multidimensional objects to develop efficient algorithms or to analyze system behavior. However, human beings are habituated to at most three-dimensional objects. In this paper, we propose a novel two-dimensional representation of the hypercube structure. The proposed representation is used to design routing and broadcasting algorithms. Finally, a comparison of the proposed representation with the conventional hypercube representation is elucidated. its fault tolerance and modularity [2,3]. There are simple and efficient algorithms for node-to-node communication, broadcasting, and other forms of communication in the hypercube [4]. Several variations of hypercube topology have been developed which further improve some of its properties. These include the twisted cube [5], cube connected cycles [6], bridged hypercube [7], generalized hypercubes [8], and binary orthogonal multiprocessors [9]. Several commercially available machines including Intel, N-Cube, and Thinking Machine as well as the Caltech Cosmic Cub have their communication network configured as a 1383-7621/0165-6074/98/$19.00

Hypercube computing: Connected components

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.

A Note on ``Generalized Hypercube and Hyperbus Structures for a Computer Network

IEEE Transactions on Computers, 1991

A general class of hypercube structures is presented in this paper for interconnecting a network of microcomputers in parallel and distributed environments. The interconnection is based on a mixed radix number system and the technique results in a variety of hypercube structures for a given number of processors No depending on the desired diameter of the network. A cost optimal realization is obtained through a process of discrete optimization. The performance of such a structure is compared to that of other existing hypercube structures such as Boolean n-cube and nearest neighbor mesh computers.

Extended Hypercube: A Hierarchical Interconnection Network of Hypercubes

Parallel and Distributed Systems, …, 1992

A new interconnection topology-the extended hypercube-consisting of an interconnection network of k-cubes is discussed. The extended hypercube is a hierarchical, expansive, recursive structure with a constant predefined building block. The extended ...

A versatile ring-connected hypercube

IEEE Micro, 1994

Our work i n deriving and comparing the reliability formulas for three leading hypercubic models-the original hypercube, Shih's cube, and the ring-connected hypercube demonstrates the superiority of the RCH approach. Though it needs twice the links of the original hypercube network, which is the best result to date, the RCH can recover h m node faihues. The higher resultant reliability of this fault-tolerant architecture makes the RCH an attractive candidate for many critical parallel-computation applications.

Dynamic shortest path algorithms for hypergraphs

… and Optimization in …, 2012

A hypergraph is a set V of vertices and a set of non-empty subsets of V , called hyperedges. Unlike graphs, hypergraphs can capture higher-order interactions in social and communication networks that go beyond a simple union of pairwise relationships. In this paper, we consider the shortest path problem in hypergraphs. We develop two algorithms for finding and maintaining the shortest hyperpaths in a dynamic network with both weight and topological changes. These two algorithms are the first addressing the fully dynamic shortest path problem in a general hypergraph. They complement each other by partitioning the application space based on the nature of the change dynamics and the type of the hypergraph. We analyze the time complexity of the proposed algorithms and perform simulation experiments for both random geometric hypergraphs and the Enron email data set. The latter illustrates the application of the proposed algorithms in social networks for identifying the most important actor based on the closeness centrality metric.

Hypermeshes: implementation and performance

Journal of Systems Architecture, 2002

Common multicomputer networks, including the torus, mesh, and hypercube, are graph topologies where a channel interconnects exactly two nodes. Hypergraphs are generalisations of the graph model, where a channel interconnects an arbitrary number of nodes. The spanning-bus hypercube is a well-known network that belongs to the hypergraph family. Regular multidimensional hypergraphs, also known as hypermeshes, have been proposed as potential alternatives to traditional graph networks for future multicomputers due to their superior topological and performance features. This paper compares the different schemes that have been proposed in the literature for implementing the hypermesh. The results reveal that one particular version of the hypermesh, known as the distributed crossbar switch hypermesh, provides the best performance when implementation costs are taken into account.

DIRECTED HYPERGRAPHS AND APPLICATIONS

Discrete Applied Mathematics, 1992

We deal with directed hypergraphs as a tool to model and solve some classes of problems arising in Operations Research and in Computer Science. Concepts such as connectivity, paths and cuts are defined. An extension of the main duality results to a special class of hypergraphs is presented. Algorithms to perform visits of hypergraphs and to find optimal paths are studied in detail. Some applications arising in propositional logic, And-Or graphs, relational data bases and transportation analysis are presented.