Interconnection Networks For Parallel Computers Research Articles

Efficient Collective Communications in Dual-Cube

The hypercube, or n-cube, has been widely used as the interconnection network in parallel computers. However, the major drawback of the hypercube is the increase in the number of communication links for each node with the increase in the total number of nodes in the system. This paper introduces a new interconnection network, namely dual-cube, for large-scale parallel computers and describes the algorithms for efficient collective communications in dual-cube. The dual-cube network mitigates the problem of increasing number of links in the large-scale hypercube network while retains hypercube’s topological properties. Design of efficient routing algorithms for collective communications is the key issue for any interconnection network. In this paper, we show that the collective communications can be done in dual-cube with almost the same communication times as in hypercube.

Homogeneous routing for homogeneous traffic patterns on meshes

The performance analysis of dynamic routing algorithms in interconnection networks of parallel computers has thus far predominantly been done by simulation studies. A limitation of simulation studies is that they usually only hold for specific combinations of network, routing algorithm, and traffic pattern. In this paper, we derive saturation point results for the class of homogeneous traffic patterns and a large class of routing functions on meshes. We show that the best possible saturation point on a mesh is half the best possible saturation point on a torus. We also show that, if we restrict ourselves to homogeneous routing functions, the worst possible saturation point on a mesh is again half the best possible saturation point. Finally, we present a class of homogeneous routing functions, containing the well-known e-cube routing function, which are all optimal for all homogeneous traffic patterns.

Index-Shuffle Graphs

Index-shuffle graphs are introduced as candidate interconnection networks for parallel computers. The comparative advantages of index-shuffle graphs over the standard bounded-degree "approximations" of the hypercube, namely butterfly-like and shuffle-like graphs, are demonstrated in the theoretical framework of graph embedding and network emulations. An N-node index-shuffle graph emulates: • an N-node shuffle-exchange graph with no slowdown, which the currently best emulations of shuffle-like graphs by hypercubes and butterflies incur a slowdown of Ω( log N). • its like-sized butterfly graph with a slowdown O( log log log N), while the currently best emulations of butterfly-like graphs by shuffle-like graphs incur a slowdown of Ω( log log N). • an N-node hypercube that executes an on-line leveled algorithm with a slowdown O( log log N), while the slowdown of currently best such emulations of the hypercube by its bounded-degree shuffle-like and butterfly-like derivatives remains Ω( log N). Our emulation is based on an embedding of an N-node hypercube into an N-node index-shuffle graph with dilation O( log log N), while the currently best embeddings of the hypercube into its bounded-degree shuffle-like and butterfly-like derivatives incur a dilation of Ω( log N).

A Super-cube Interconnection NetworkFor Parallel Computers

In this paper, we consider some interconnection networks for parallel computers. Let d be the greatest distance in a network, and let / be the maximum number of circuits connected from optional processor. It is well known, for the hypercube interconnection network, d = Iog2%, / = Iog2?%, where n is the number of processors in the network. In this paper, we present a super-cube interconnection network for parallel computers. For this new interconnection network, d and / both satisfies d < 0.86 logg n and / < 0.86 log n.

Fault-tolerant cube graphs and coding theory

Hypercubes, meshes, tori, and Omega networks are well-known interconnection networks for parallel computers. The structure of those graphs can be described in a more general framework called cube graphs. The idea is to assume that every node in a graph with q/sup l/ nodes is represented by a unique string of l symbols over GF(q). The edges are specified by a set of offsets, those are vectors of length l over GF(q), where the two endpoints of an edge are an offset apart. We study techniques for tolerating edge faults in cube graphs that are based on adding redundant edges. The redundant graph has the property that the structure of the original graph can be maintained in the presence of edge faults. Our main contribution is a technique for adding the redundant edges that utilizes constructions of error-correcting codes and generalizes existing ad hoc techniques.

Optical binary de Bruijn networks for massively parallel computing: design methodology and feasibility study

The interconnection network structure can be the deciding and limiting factor in the cost and the performance of parallel computers. One of the most popular point-to-point interconnection networks for parallel computers today is the hypercube. The regularity, logarithmic diameter, symmetry, high connectivity, fault tolerance, simple routing, and reconfigurability (easy embedding of other network topologies) of the hypercube make it a very attractive choice for parallel computers. Unfortunately the hypercube possesses a major drawback, which is the complexity of its node structure: the number of links per node increases as the network grows in size. As an alternative to the hypercube, the binary de Bruijn (BdB) network has recently received much attention. The BdB not only provides a logarithmic diameter, fault tolerance, and simple routing but also requires fewer links than the hypercube for the same network size. Additionally, a major advantage of the BdB network is a constant node degree: the number of edges per node is independent of the network size. This makes it very desirable for large-scale parallel systems. However, because of its asymmetrical nature and global connectivity, it poses a major challenge for VLSI technology. Optics, owing to its three-dimensional and globalconnectivity nature, seems to be very suitable for implementing BdB networks. We present an implementation methodology for optical BdB networks. The distinctive feature of the proposed implementation methodology is partitionability of the network into a few primitive operations that can be implemented efficiently. We further show feasibility of the presented design methodology by proposing an optical implementation of the BdB network.

Wildcard dimensions, coding theory and fault-tolerant meshes and hypercubes

Hypercubes, meshes and tori are well known interconnection networks for parallel computers. The sets of edges in those graphs can be partitioned to dimensions. It is well known that the hypercube can be extended by adding a wildcard dimension resulting in a folded hypercube that has better fault-tolerant and communication capabilities. First we prove that the folded hypercube is optimal in the sense that only a single wildcard dimension ran be added to the hypercube. We then investigate the idea of adding wildcard dimensions to d-dimensional meshes and tori. Using techniques from error correcting codes we construct d-dimensional meshes and tori with wildcard dimensions. Finally, we show how these constructions can be used to tolerate edge and node faults in mesh and torus networks. >

RH: a versatile family of reduced hypercube interconnection networks

The binary hypercube has been one of the most frequently chosen interconnection networks for parallel computers because it provides low diameter and is so robust that it can very efficiently emulate a wide variety of other frequently used networks. However, the major drawback of the hypercube is the increase in the number of communication channels for each processor with an increase in the total number of processors in the system. This drawback has a direct effect on the very large scale integration complexity of the hypercube network. This short note proposes a new topology that is produced from the hypercube by a uniform reduction in the number of edges for each node. This edge reduction technique produces networks with lower complexity than hypercubes while maintaining, to a high extent, the powerful hypercube properties. An extensive comparison of the proposed reduced hypercube (RH) topology with the conventional hypercube is included. It is also shown that several copies of the popular cube-connected cycles network can be emulated simultaneously by an RH with dilation 1. >