Sharif Digital Repository

We study a class of interconnection networks for multiprocessors, called the Stretched-G network, which is based on the base graph G by replacing each edge of the base network with an array of processors. Two interesting features of the proposed topology are its area-efficient VLSI layout and superior scalability over the underlying base network while preserving most of its desirable properties. We conduct a general study on the topological properties of stretched networks. We first obtain their basic topological parameters, after that we present an optimal routing algorithm. We also present a unified approach to obtain the topological properties and the VLSI-layout of an arbitrary stretched... 

Parallel computers, such as multiprocessors system-on-chip (Mp-SoCs), multicomputers and cluster computers, are consisting of hundreds or thousands multiple processing units and components (such as routers, channels and connectors) connected via some interconnection network that collectively may undergo high failure rates. Therefore, these systems are required to be equipped with fault-tolerant mechanisms to ensure that the system will keep running in a degraded mode. Normally, the faulty components are coalesced into fault regions, which are classified into two major categories: convex and concave regions. In this paper, we propose the first solution to calculate the probability of... 

Many fully-adaptive algorithms have been proposed to overcome the performance limitations of deterministic routing in networks used in high-performance multicomputers, such as the well-known regular n-D torus. This paper proposes a simple yet reasonably accurate analytical performance model to predict message communication latency in tori networks. This model requires a running time of O(1) which is the fastest model yet reported in the literature. Extensive simulations reveal that the new performance model maintains a reasonable accuracy when the network operates under different traffic conditions. The model is then used to perform an extensive investigation into the performance merits of... 

The Pyramid network is a desirable network topology used as both software data-structure and hardware architecture. In this paper, we propose a general definition for a class of pyramid networks that are based on grid connections between the nodes in each level. Contrary to the conventional pyramid network in which the nodes in each level form a mesh, the connections between these nodes may also be according to other grid-based topologies such as the torus, hypermesh or WK-recursive. Such pyramid networks form a wide class of interconnection networks that possess rich topological properties. We study a number of important properties of these topologies for general-purpose parallel processing... 

The star graph was introduced as an attractive alternative to the well-known hypercube and its properties have been well studied in the past. Most of these studies have focused on topological properties and algorithmic aspects of this network. In this paper, the performance of nine fully-adaptive routing algorithms in the star network are studied under uniform (with and without locality) and hotspot traffic patterns. The performance factors considered are the average message latency and network utilization. We consider three basic routing algorithms (two hop scheme routing algorithms: positive-hop and negative-hop, and Msic's routing algorithm) and two other improved sets of improved... 

The three dimensional discrete cosine transform (3D DCT) has been widely used in many applications such as video compression. On the other hand, the kary n-cube is one of the most popular interconnection networks used in many recent multicomputers. As direct calculation of 3D DCT is very time consuming, many researchers have been working on developing algorithms and special-purpose architectures for fast computation of 3D DCT. This paper proposes a parallel algorithm for efficient calculation of 3D DCT on the k-ary n-cube multicomputers. The time complexity of the proposed algorithm is of O(N) for an N × N × N input data cube while direct calculation of 3D DCT has a complexity of O(N6). ©... 

In this paper, we introduce a new class of interconnection networks for multiprocessor systems which we refer to as Stretched-Hypercubes, or shortly the Stretched-Cube networks. These networks are obtained by replacing an edge of the well-known hypercube network with an array of processors. Two interesting features of the proposed topology are its area-efficient VLSI layout and superior scalability over the traditional hypercube network. Some topological properties of the proposed network are studied. In addition, an area-efficient VLSI layout for the stretched-cube is suggested and some comparisons between the proposed network and previously studied networks such as the star and hypercube... 

We study a class of interconnection networks for multiprocessors, called the Necklace-G network that is based on the base graph G by attaching an array of processors to each two adjacent nodes of G. One of the interesting features of the proposed topology is its scalability while preserving most of the desirable properties of the underlying base network G. We conduct a general study on the topological properties of necklace networks. We first obtain their basic topological parameters, and then present optimal routing and broadcasting algorithms. We also present a unified approach to obtain the topological properties and the VLSI-layout of an arbitrary necklace network based on the properties... 

In optoelectronic OTIS architectures, electrical and optical interconnects are used for local and global communication, respectively. Interesting instances of the OTIS architecture are the OTIS-hypercube and OTIS-mesh. This paper conducts a performance evaluation and comparison of these networks under different structural conditions and traffic loads. All judgments made, are based on observations from extensive simulation results of the interconnection networks. We conclude that, when the OTIS-hypercube and equivalent 2-D OTIS-mesh are compared under the constraint of equal bisection bandwidth, the performance of the OTIS-hypercube is of superior performance. We however show that the... 

Most of previous studies have assessed the performance issues for regular buffer and virtual channel organiza-tions and have not considered overall buffer size constraint. In this paper, the performance of mesh-based interconnection networks (mesh, torus and hypercube networks) under different traffic patterns (uniform, hotspot, and matrix-transpose) is studied. We investigate the effect of the number of virtual channels and their buffer lengths, on the performance of these topologies when the total buffer size associated to each physical channel (and thus router buffer size) is fixed.The results show that the optimal number of virtual channels and buffer length highly depends on the traffic... 

Many theoretical studies have compared the hypercube and star graphs from a graph theoretical viewpoint, under structural and algorithmic properties. None of these studies have, however, considered real working conditions and implementation constraints. In this paper, the hypercube and star graphs are compared in view of fault tolerance and technological implementation constraints. In order to realize a fair comparison, we use the unsafely-vector fault tolerant routing algorithm, recently introduced in [1] and [2], for the hypercube and star graph. Under two implementation constraints, namely constant bisection bandwidth and constant node pin-out, we have compared the performance of the two... 

This paper introduces a new class of interconnection networks named Star-Pyramid, SP(n). A star-pyramid of dimension n is formed by piling up star graphs of dimensions 1 to n in a hierarchy, connecting any node in each i-dimensional star, 1< i ≤ n, to a node in (i - 1)-star whose index is reached by removing the i symbol from the index of the former node in the i-star graph. Having extracted the properties of the new topology, featuring topological properties, a simple routing algorithm and Hamiltonicity then we compare the network properties of the proposed topology and the well-known pyramid topology. We show that the star-pyramid is more fault-tolerant and has less network diameter than... 

In this paper, a parallel algorithm for data clustering is presented on a multi-computer with star topology. This algorithm is fast and requires a small amount of memory per processing element, which makes it even suitable for SIMD implementation. The proposed parallel algorithm completes in O(K+S 2-T 2) steps for a clustering problem of N data patterns with M features per pattern and K clusters, where N.M = S!, K.M = T!, and M=R!, on a s-star interconnection network. © Springer-Verlag Berlin Heidelberg 2005  

In this paper, we propose a new modular topology for interconnection networks, the Recursive Transpose-Connected Cycles (RTCC). The RTCC has a recursive definition quite similar to that of fractal graphs having interesting topological characteristics, making it suitable for utilization as the base topology of large-scale multicomputer interconnection networks. We study important properties of this topology such as diameter, bisection width and issues related to implementation, such as routing algorithms and the average message latency under VLSI layout constraints. In addition, we prove that the RTCC is a Hamiltonian graph, We conclude that, insight of most of the above-mentioned properties,... 

Several analytical models of fully adaptive routing (AR) in wormhole-routed networks have recently been reported in the literature. All these models, however, have been discussed for routing algorithms with deadlock avoidance. Recent studies have revealed that deadlocks are quite rare in the network, especially when enough routing freedom is provided. Thus the hardware resources, e.g. virtual channels, dedicated for deadlock avoidance are not utilised most of the time. This consideration has motivated researchers to introduce fully adaptive routing algorithms with deadlock recovery. This paper describes a new analytical model of a true fully AR algorithm with software-based deadlock... 

Several studies have examined the relative performance merits of the torus and hypercube taking into account the channel bandwidth constraints imposed by implementation technology. While the torus has been shown to outperform the hypercube under the constant wiring density constraint, the opposite conclusion has been reached when the constant pin-out constraint is considered. However, all these studies have assumed deterministic routing and have not taken into account the internal hardware cost of routers. This paper re-examines the performance merits of the torus and hypercube using both fully-adaptive and deterministic routing strategies. Moreover, it uses a new cost model which takes into... 

Several studies have examined the relative performance merits of the torus and hypercube taking into account the channel bandwidth constraints imposed by implementation technology. While the torus has been shown to outperform the hypercube under the constant wiring density constraint, the opposite conclusion has been reached when the constant pin-out constraint is considered. However, these studies have assumed a pure uniform traffic pattern and deterministic routing. The 'uniform traffic' assumption is not always justifiable in practice as there are many real-world parallel applications that exhibit non-uniform traffic patterns, which can create unbalanced traffic such as hotspots in the... 

Several analytical models of fully adaptive routing in wormhole-routed k-ary n-cubes under the uniform traffic pattern have recently been proposed in the literature. Although the uniform reference model has been widely used in the past, it is not always true in practice as there are many applications that exhibit non-uniform traffic patterns. There has not been so far any study that describes an analytical model of fully adaptive routing under non-uniform traffic conditions. This paper describes a new analytical model of fully adaptive routing in k-ary n-cubes in the presence of non-uniform traffic generated by matrix-transpose permutations, which is an important communication operation... 

Although several analytical models have been proposed in the literature for binary n-cubes with deterministic routing, most of them have not included the effects of virtual channel multiplexing on network performance. The only mathematical model for deterministic wormhole routing in hypercubes with virtual channels was proposed in [Y. Boura, Design and Analysis of Routing Schemes and Routers for Wormhole-routed Mesh Architectures, Ph.D. Thesis, Department of Computer Science and Engineering, Pennsylvania State University, 1995] which uses complex combinatorial analysis with a computation time of O(N = 2n) for an n-dimensional hypercube. This paper proposes a new and simple analytical model... 

This paper introduces a parallel algorithm for computing an N = n2n point Lagrange interpolation on an n-dimensional cube-connected cycles (CCCn). The algorithm consists of three phases: initialisation, main and final. While there is no computation in the initialisation phase, the main phase is composed of n2n-1 steps, each consisting of four multiplications, four subtractions and one communication operation, and an additional step including one division and one multiplication. The final phase is carried out in two sub-phases. There are [n/2] steps in the first sub-phase, each including two additions and one communication, followed by the second sub-phase which comprises n steps each...