Class Of Interconnection Networks Research Articles

Strong matching preclusion problem of the folded Petersen cube

ABSTRACTA strong matching preclusion set in a graph is a set of vertices and edges whose removal leaves the graph with no perfect matchings or almost perfect matchings. The strong matching preclusion number of a graph is the minimum cardinality of a strong matching preclusion set. The notion of strong matching preclusion was introduced by Park and Ihm as an extension of the matching preclusion problem, where only edges may be deleted. The folded Petersen cubes are a class of interconnection networks, formed by iterated Cartesian products of the well-known Petersen graph and the complete graph , which possess many desirable properties. In this paper, we find the strong matching preclusion number of the folded Petersen cubes and categorize all optimal strong matching preclusion sets of these graphs. To do so, we develop and utilize more general results related to strong matching preclusion for graphs formed by Cartesian products of particular graphs.

Optimal Routing Algorithm in Multilayer Octagon-Cell: A New Class of Octagon-Cell Interconnected Networks

In communication system of network routing algorithm acts an important role. The efficiency of a parallel system depends on the reliable and efficient routing algorithm which is used to route the messages between the fault-free nodes. In this paper a new class of interconnection network of Octagon-Cell is introduced, which is called Multilayer Octagon-Cell (MLO). The structure of Multilayer Octagon-cell is recursive in nature. It can be expanded, if we increase the depth of MLO. This paper introduces the node degree, diameter, number of links, bisection width of the MLO network and we have also developed the optimal routing algorithm of MLO.

Strong Matching Preclusion of Arrangement Graphs

The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph with neither perfect matchings nor almost-perfect matchings. This is an extension of the matching preclusion problem that was introduced by Park and Ihm. The class of arrangement graphs was introduced as a common generalization of the star graphs and alternating group graphs, and to provide an even richer class of interconnection networks. In this paper, the goal is to find the strong matching preclusion number of arrangement graphs and to categorize all optimal strong matching preclusion sets of these graphs.

On the Conditional Diagnosability of Hyper-Buttery Graphs and Related Networks

The conditional diagnosability is an important measure of reliability of interconnection networks. Much progress has been made in the past decade. By consolidating various results, a general scheme can be developed to solve the conditional diagnosability problem for many important classes of interconnection networks; thus eliminating various ad-hoc methods used in earlier studies. The buttery network is an important interconnection network and it has been rediscovered multiple times by different authors. The hyper-buttery network is a graph that amalgamates the buttery network and the hypercube. In this paper, we solve the conditional diagnosability problem for these hyper-buttery networks and their generalizations.

GreedyZero Algorithms for Conflict-free Scheduling in Low Stage Interconnection Network

Abstract Low Stage Interconnection Networks are a class of Interconnection Networks. They have been generated from Multistage Interconnection Networks (MINs). Although the conflict in the optical switches, there is the consid- erable interest to use the optical technology in interconnection networks implementation. To avoid this problem, GreedyZero algorithms has been assigned to the Low Stage Interconnection Networks for improving the network performance by reducing the number of passes. The results marked nearly 50% reduction in the number of passes and proved improvement of scheduling in the Low Stage Interconnection Networks by GreedyZero algorithms.

The Wiener Index of Circulant Graphs

Circulant graphs are an important class of interconnection networks in parallel and distributed computing. In this paper, we discuss the relation of the Wiener index and the Harary index of circulant graphs and the largest eigenvalues of distance matrix and reciprocal distance matrix of circulants. We obtain the following consequence:W/λ=H/μ;2W/n=λ;2H/n=μ, whereW,Hdenote the Wiener index and the Harary index andλ,μdenote the largest eigenvalues of distance matrix and reciprocal distance matrix of circulant graphs, respectively. Moreover we also discuss the Wiener index of nonregular graphs with cut edges.

CONDITIONAL MATCHING PRECLUSION FOR (n,k)-STAR GRAPHS

The matching preclusion number of an even graph G, denoted by mp (G), is the minimum number of edges whose deletion leaves the resulting graph without perfect matchings. The conditional matching preclusion number of an even graph G, denoted by mp 1(G), is the minimum number of edges whose deletion leaves the resulting graph with neither perfect matchings nor isolated vertices. The class of (n,k)-star graphs is a popular class of interconnection networks for which the matching preclusion number and the classification of the corresponding optimal solutions were known. However, the conditional version of this problem was open. In this paper, we determine the conditional matching preclusion for (n,k)-star graphs as well as classify the corresponding optimal solutions via several new results. In addition, an alternate proof of the results on the matching preclusion problem will also be given.

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.

Multilayer Hex-Cells: A New Class of Hex-Cell Interconnection Networks for Massively Parallel Systems

Scalability is an important issue in the design of interconnection networks for massively parallel systems. In this paper a scalable class of interconnection network of Hex-Cell for massively parallel systems is introduced. It is called Multilayer Hex-Cell (MLH). A node addressing scheme and routing algorithm are also presented and discussed. An interesting feature of the proposed MLH is that it maintains a constant network degree regardless of the increase in the network size degree which facilitates modularity in building blocks of scalable systems. The new addressing node scheme makes the proposed routing algorithm simple and efficient in terms of that it needs a minimum number of calculations to reach the destination node. Moreover, the diameter of the proposed MLH is less than Hex-Cell network.

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

Embedding hypercubes, rings, and odd graphs into hyper-stars

Hypercubes and star graphs are two of the most fundamental classes of interconnection networks. The class of hyper-stars was introduced as a hybrid of these two classes. In this note, we establish topological relationship between the hyper-stars and three known classes of networks, namely, hypercubes, tori and odd graphs, via embedding.

Strongly Diagnosable Systems under the Comparison Diagnosis Model

A system is t-diagnosable if all faulty nodes can be identified without replacement when the number of faults does not exceed t, where t is some positive integer. Furthermore, a system is strongly t-diagnosable if it is t-diagnosable and can achieve (t+1)-diagnosable except for the case where a node's neighbors are all faulty. In this paper, we propose some conditions for verifying whether a class of interconnection networks, called matching composition networks (MCNs), are strongly diagnosable under the comparison diagnosis model.

Matching preclusion for some interconnection networks

AbstractThe matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost‐perfect matchings. In this paper, we find this number for various classes of interconnection networks and classify all the optimal solutions. © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 50(2), 173–180 2007

Interconnection Networks and Their Eigenvalues

Interconnection networks of various topologies have been widely used in designing multiprocessor architectures. Study of graph theoretical or combinatorial properties of such networks help us better understand them, as well as develop on these architectures more efficient parallel algorithms including fault-tolerant communication/routing algorithms. In this paper, we analyze a broad class of interconnection networks from a new angle by looking into the corresponding graph spectra (i.e., eigenvalues and their multiplicities). Since eigenvalues of the edjacency matrix of a graph can reveal many important properties of the graph that are closely related to its combinatorial invariants, we believe that the study of spectra of interconnection networks can be a more unified approach to studying their topological properties. As a first step) in this direction, here we mainly concentrate on finding out the spectra of some of the most studied interconnection networks. Specifically, after a brief survey of results that relate spectra of graphs to their structural properties, we summarize the existing results for eigenvalues and multiplicities of several popular interconnection networks such as the hypercube and mesh. We also derive some of these results in a more straightforward way. Then we present new results on spectra for some other known networks such as the line graph of the hypercube, followed by experimental results on a few others including the star and pancake networks.

Fast permutation routing in a class of interconnection networks

AbstractThis paper considers the following permutation routing problem: Given an N × N augmented data manipulator (ADM) network and a permutation π between its N inputs and outputs, can all the traffic connections of π be routed through the network in one pass? A number of backtrack search algorithms have been devised for recognizing ADM admissible permutations. None of the published results, however, appears to settle the time complexity of the problem. The goal of this paper was to answer the question positively by showing the first polynomial time bound for solving the problem. The devised algorithm requires O(N1.695) time to decide whether a given permutation π is admissible and compute a setting of the switches whenever π is admissible. For many practical applications, the obtained bound compares favorably with the O(N lg N) size of an N‐input ADM network. © 2002 Wiley Periodicals, Inc.

Recursive diagonal torus: an interconnection network for massively parallel computers

Recursive Diagonal Torus (RDT), a class of interconnection network is proposed for massively parallel computers with up to 2/sup 16/ nodes. By making the best use of a recursively structured diagonal mesh (torus) connection, the RDT has a smaller diameter (e.g., it is 11 for 2/sup 10/ nodes) with a smaller number of links per node (i.e., 8 links per node) than those of the hypercube. A simple routing algorithm, called vector routing, which is near-optimal and easy to implement is also proposed. Although the congestion on upper rank tori sometimes degrades the performance under the random traffic, the RDT provides much better performance than that of a 2D/3D torus in most cases and, under hot spot traffic, the RDT provides much better performance than that of a 2D/3D/4D torus. The RDT router chip which provides a message multicast for maintaining cache consistency is available. Using the 0.5 /spl mu/m BICMOS SOG technology, versatile functions, including hierarchical multicasting, combining acknowledge packets, shooting down/restart mechanism, and time-out/setup mechanisms, work at a 60 MHz clock rate.

FAULT-TOLERANT COMMUNICATIONS ON HYPERCUBE-CLUSTERS

Hierarchical interconnection networks with n-dimensional hypercube clusters can strike a balance between wide application suitability, size scalability as well as reliability. Cluster communications support for such networks must therefore be reliable and efficient without incurring large overheads. This paper proposes a reliable and cost-effective intra-cluster communications strategy for such a class of interconnection networks. The routing algorithm can tolerate up to (n - 1) component faults in the cluster and generates routes that are cycle-free and livelock-free. The message is guaranteed to be optimally (respectively, sub-optimally) delivered within a maximum of n (respectively, 2n - 1) hops. The message overhead incurred is one of the lowest reported for the specified fault tolerance level – with only a single n-bit routing vector accompanying the message to be communicated. Finally, routing hardware support may be simply achieved with standard components, facilitating integration with the host network.

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.

UNIFIED PARALLEL ALGORITHMS FOR GAUSSIAN ELIMINATION WITH BACKWARD SUBSTITUTION ON PRODUCT NETWORKS

The increasing interest in product networks (PNs) as a method of combining desirable properties of component networks, has prompted a need for the general study of the algorithmic issues related to this important class of interconnection networks. In this paper we present unified parallel algorithms for Gaussian elimination, with partial and complete pivoting, on product networks. A parallel algorithm for backward substitution is also presented. The proposed algorithms are network independent and are also independent of the matrix distribution methods employed. These algorithms can be used on a wide range of PNs including hypercube, mesh, and k-ary n-cube. Unified models for estimating computation time and interprocessor communication time are also presented. These models are then used to measure the performance of the proposed algorithms on several product networks

Performance evaluation of a bus-based multistage multiprocessor architecture

This paper proposes and evaluates a class of interconnection networks, which provide performance comparable to a multiple bus network with considerably lower cost. These networks, referred to as hybrid networks, are formed by beginning with a multistage network and substituting buses in the second stage. Analytic models are developed to evaluate the performance of the system. The analysis includes both uniform and non-uniform distribution of requests. The results obtained are compared with simulation results.