Multicomputer Interconnection Networks Research Articles

Irregular chromatic number for hypercube graph and its variants

The attractive properties of the hypercube graph such as its diameter, good connectivity, and symmetry have made it a popular topology for the design of multi-computer interconnection networks. Efforts to improve some of these properties have led to the evolution of hypercube variants. Let c be the proper coloring of graph G, where the neighboring vertices will get individual colors. Coloring c is irregular if distinct vertices have distinct color codes and the least number of colors that ought to receive an irregular coloring is the irregular chromatic number, χir (G). In this paper, we discuss the irregular coloring and find the irregular chromatic number for the hypercube graph Qn and some of its variants using binomial coefficients for the Locally twisted cube graph LTQn, Crossed cube graph CQn and two types of Fractal cubic network graph FCNG1 (k) and FCNG2 (k).

Improving system performance in non-contiguous processor allocation for mesh interconnection networks

Contiguous allocation of parallel jobs in multicomputers usually suffers from the degrading effects of fragmentation, because it requires that the allocated processors be contiguous and have the same topology as that of the multicomputer's interconnection network. Fragmentation can be avoided by adopting non-contiguous allocation. However, non-contiguous allocation can increase the distances among processors allocated to a job, which can increase the interference among messages of different jobs and increases message contention and delays. This paper suggests a new non-contiguous processor allocation strategy, referred to as Minimum Interference Paging (MIP), for the 2D mesh network. MIP attempts to reduce the distances among processors allocated using a paging variant that chooses a set of processors with the lowest distance between the first and last allocated processors, where the distance is the number of processors between the first allocated node and last allocated node. Using software simulation, we compared the performance of MIP against that of several well-known non-contiguous allocation strategies: paging (0), Multiple Buddy System (MBS) and Adaptive Non-contiguous Allocation (ANCA). The comparative evaluation was conducted using First-Come-First-Served (FCFS) job scheduling, wormhole routing and six communication patterns. These are the one-to-all, all-to-all, Near Neighbour, Ring, Divide and Conquer Binomial Tree (DQBT), and Random communication patterns. The results show that MIP exhibits superior performance in terms of average turnaround time of jobs.

An accurate performance model for network-on-chip and multicomputer interconnection networks

In this paper, we present a mathematical background for a new approach for performances modeling of interconnection networks, based on analyzing the packet blocking and waiting time spent in each channel passing through all possible paths in the channel dependency graph. We have proposed a new, simple and very accurate analytical model for deterministic routing in wormhole networks, which is general in terms of the network topology and traffic distribution. An accurate calculation of the variance of the service time has been developed, which overcomes the rough approximation used, as a rule, in the existing models. The model supports two-dimensional mesh topologies, widely used in network-on-chip architectures, and multidimensional topologies, popular in multicomputer architectures. It is applicable even for irregular topologies and arbitrary application-specific traffic. Results obtained through simulation show that the model achieves a high degree of accuracy.

A New Addressing Schema for Mapping Honeycomb into Different Topologies

In a parallel system, nodes communicate with each other by exchanging messages. Different topologies exist for arranging processors in a network based on the architecture of the network; or based on the fact that a network is a multiprocessor or multi computer network. A honeycomb network is considered as a multiprocessor / multi-computer interconnection network where each node represents a processor/computer and each line represents a link between two computers. In this paper a new addressing schema is presented for the honeycomb network; which can be used in many levels. The rest of the paper defines some methods of mapping the honeycomb into bus, tree, grid in addition to a proposed cluster-based architecture. Mapping the honeycomb requires however some compromising; such as ignoring some links or adding others. Recent patent and research advances aim to find methods for reducing the complexity of mapping honeycomb into other topologies.

The triangular pyramid: Routing and topological properties

In this paper, a new topology for multicomputer interconnection networks, based on triangular mesh, is proposed. The new network, referred to as the triangular pyramid (or tripy for short), has L levels of triangular mesh. We study some basic important properties of the proposed network as well as introduce a routing algorithm for the tripy network based on the routing of triangular meshes. We prove that this form of pyramidal network is Hamiltonian, Hamiltonian-connected, and pancyclic. We also prove that the proposed network is 6-colorable and conduct a brief comparison of the tripy and its traditional pyramid counterpart. Our results show that the proposed network has higher scalability, connectivity, and total network bandwidth while preserving the important properties of the traditional pyramid network.

Stochastic Analysis of Deterministic Routing Algorithms in the Presence of Self-Similar Traffic

Many performance models for deterministic routing in multicomputer interconnection networks have been derived and analyzed under the assumption of the traditional Poisson stochastic arrival process, which is inherently unable to capture traffic self-similarity revealed by many real-world parallel applications. In an effort towards understanding the network performance under various traffic loads and different design alternatives, this paper presents an analytical model for dimension-ordered routing in k-ary n-cubes when subjected to self-similar traffic. As the service time, blocking probability and waiting time experienced by a message vary from a dimension to another, the design of such a model for dimension-ordered routing poses greater challenges. The developed analytical model is then used to investigate the efficiency of two different ways to organize virtual channels for deterministic routing and to evaluate the impact of self-similar traffic with various Hurst parameters on network performance.

VLSI Photonic Ring Multicomputer Interconnect: Architecture and Signal Processing Performance

This paper presents the architectural design of a multicomputer interconnection network based on the use of optical technology. The performance of the system is evaluated on a set of signal processing applications. The interconnect uses Vertical Cavity Surface Emitting Lasers (VCSELs) and flexible fiber image guides to implement a physical ring topology that is logically configured as a multiring. Processors in the multicomputer are nodes on the ring and extremely high communication bandwidth is possible. Using the Laser Channel Allocation (LCA) algorithm and the Deficit Round Robin (DRR) media access protocol, the bandwidth available in the optical interconnect can be reconfigured to make efficient use of the interconnect resources. A discrete-event simulation model of the interconnect is used to examine performance issues such as throughput, latency, fairness, and the impact of reconfigurability.

On the performance of multicomputer interconnection networks

Several researchers have analysed the performance of k -ary n -cubes taking into account channel bandwidth constraints imposed by implementation technology, namely the constant wiring density and pin-out constraints for VLSI and multiple-chip technology respectively. For instance, Dally [IEEE Trans. Comput. 39(6) (1990) 775], Abraham [Issues in the architecture of direct interconnection networks schemes for multiprocessors, Ph.D. thesis, University of Illinois at Urbana-Champaign, 1992], and Agrawal [IEEE Trans. Parallel Distributed Syst. 2(4) (1991) 398] have shown that low-dimensional k -ary n -cubes (known as tori) outperform their high-dimensional counterparts (known as hypercubes) under the constant wiring density constraint. However, Abraham and Agrawal have arrived at an opposite conclusion when they considered the constant pin-out constraint. Most of these analyses have assumed deterministic routing, where a message always uses the same network path between a given pair of nodes. More recent multicomputers have incorporated adaptive routing to improve performance. This paper re-examines the relative performance merits of the torus and hypercube in the context of adaptive routing. Our analysis reveals that the torus manages to exploit its wider channels under light traffic. As traffic increases, however, the hypercube can provide better performance than the torus. Our conclusion under the constant wiring density constraint is different from that of the works mentioned above because adaptive routing enables the hypercube to exploit its richer connectivity to reduce message blocking.

Towards scalable collective communication for multicomputer interconnection networks

A considerable number of broadcast algorithms have been proposed for the mesh over the past decade. Nonetheless, most of these algorithms do not exhibit good scalability properties as the network size increases. As a consequence, most existing broadcast algorithms cannot efficiently support real-world parallel applications that require large-scale system sizes due to their high computational demands. Motivated by these observations, this paper proposes the Nearest Side First Algorithm (or NSF for short) as a new adaptive broadcast algorithm for the mesh. One of the key results is that the performance of the NSF algorithm scales up well with the increase of processing elements, a feature not demonstrated by any previous broadcast algorithms, which enables the proposed algorithm to utilise massive parallel architectures with maximum effectiveness.

Analysis of k-ary n-cubes with dimension-ordered routing

K-ary n-cubes have been one of the most popular interconnection networks for practical multicomputers due to their ease of implementation and ability to exploit communication locality found in many parallel applications. This paper describes an analytical model for k-ary n-cubes with dimension-ordered routing. The main feature of the model is its ability to captures network performance when an arbitrary number of virtual channels are used to reduce message blocking. Simulation experiments reveal that the latency results predicted by the analytical model are in good agreement with those provided by the simulation model.

A Comparison of Router Architectures for Virtual Cut-Through and Wormhole Switching in a NOW Environment

Most multicomputer interconnection networks use wormhole switching, leading to fast and compact routers. Current routers incorporate virtual channels and even fully adaptive routing. Networks of workstations (NOWs) inherited multicomputer technology. Most commercial routers designed for NOWs implement wormhole switching. However, wormhole switching is not well suited for NOWs. The long wires required in this environment lead to large buffers to prevent buffer overflow during flow control signaling. Moreover, wire length is limited by buffer size. Virtual cut-through (VCT) achieves a higher throughput than wormhole switching. However, buffer requirements and packetizing overhead prevented its widespread use in multicomputers. Nevertheless, wormhole and VCT switching require similar buffer capacity in NOWs. Moreover, some messaging layers such as Illinois Fast Messages (FM) and BIP split messages into packets for increased performance. Therefore, the traditional disadvantages of VCT switching disappear in NOWs. In this paper, we show that VCT routers can be simpler than wormhole routers, while still achieving the advantages of using virtual channels and adaptive routing. We also propose a fully adaptive routing algorithm for VCT switching in a NOW environment. Moreover, we show that VCT routers outperform wormhole routers in a NOW environment at a lower cost. Also, VCT routers require buffer capacity independent of wire length, making them suitable for networks of workstations.

On the design of hypermesh interconnection networks for multicomputers

Topology, routing algorithm, and router structure are among the most important factors that greatly influence network performance. This paper assesses the interaction of these elements on two related but distinct types of multicomputer networks, the binary n -cube (or cube) and the hypermesh. The analysis will show that the topological properties of the hypermesh confer an important advantage over the cube that makes the former a promising option for use in high-performance multicomputers. The hypermesh can use simple routing algorithms and cheap routers with little performance penalty. The cube, on the other hand, is constrained to the use of a specific routing algorithm and complex routers to take advantage of its rich connectivity.

Flexible and efficient routing based on progressive deadlock recovery

The development of fully adaptive, cut-through (wormhole) networks is important for achieving high performance in communication-critical parallel processor systems. Increased flexibility in routing allows network bandwidth to be used efficiently, but also creates more opportunity for cyclic resource dependencies to form which can cause deadlock. If not guarded against, deadlocks in routing make packets block in the network indefinitely and, eventually, could result in the entire network coming to a complete standstill. The paper presents a simple, flexible, and efficient routing approach for multicomputer interconnection networks which is based on progressive deadlock recovery as proposed to deadlock avoidance or regressive deadlock recovery. Performance is optimized by allowing the maximum routing freedom provided by network resources to be exploited. True fully adaptive routing is supported in which all physical and virtual channels at each node in the network are available to packets without regard for deadlocks. Deadlock cycles, upon forming, are efficiently broken in finite time by progressively routing one of the blocked packets through a connected, deadlock-free recovery path. This routing approach enables the design of high-throughput networks that provide excellent performance. Simulations indicate that progressive deadlock recovery routing can improve throughput by as much as 45 percent and 25 percent over leading deadlock avoidance-based and regressive recovery-based routing schemes, respectively.

‘Dead reckoning’ — a primitive and efficient self-routing protocol for ultrafast mesh networks

The authors describe a new approach to the problem of self-routing in ultra-high-speed multi-computer interconnection networks. The method is based on the concept of ‘dead reckoning’ (self-navigation without the use of landmarks), and is applicable to networks with a mainly regular mesh topology. The packet header contains, in addition to the usual destination address, a tiny amount of directional information (as little as 2 bits in the case of the Manhattan street network). With this additional data, the algorithm for path selection at the network nodes becomes extraordinarily simple, allowing very fast processing with good routing efficiency and high throughput. Most significantly, with this method it is not necessary to read each binary digit of the destination address of every packet arriving at every intermediate routing node; it is sufficient only to perform a single-stage pattern match between the packet address and the address of the routing node. This feature, and the low latency of this self-routing technique, make it particularly well suited to ultrafast photonic networks.

DESIGN AND PERFORMANCE ANALYSIS OF MULTISTAGE INTERCONNECTION NETWORKS USING A RECURSIVE MULTICAST ALGORITHM

In this paper, we study issues of the multicast communication in the multistage interconnection networks (MINs) for large-scale multicomputers. In addition to point-to-point communication among processing nodes, efficient collective communication is critical to the performance of multicomputers. Multicast communication in which the same packet is delivered from a source node to an arbitrary number of destination nodes is fundamental in supporting collective communication primitives including broadcast, reduction, and barrier synchronization operations. This paper presents a new approach to support multicast communication, on the basis of a restricted address encoding scheme which constructs a short fixed-size multicast header, and a recursive scheme that recycles a multicast packet one or more times through the MIN to send it to the desired destination nodes. We propose a recursive multicast algorithm which provides deadlock-freedom for multiple multicast packets in MIN-based multicomputers. We also present performance model for the unbuffered MIN using the multicast algorithm and analyze its performance in terms of the network throughput, where several multicast communications are considered. The proposed algorithm can be easily applied to wormhole or virtual cut-through MIN-based multicomputers.

Optimal emulations by butterfly-like networks

The power of butterfly-like networks as multicomputer interconnection networks is studied, by considering how efficiently the butterfly can emulate other networks. Emulations are studied formally via graph embeddings, so the topic here becomes : How efficiently can one embed the graph underlying a given interconnection network in the graph underlying the butterfly network ? Within this framework, the slowdown incurred by an emulation is measured by the sum of the dilation and the congestion of the corresponding embedding (respectively, the maximum amount that the embedding stretches an edge of the guest graph, and the maximum traffic across any edge of the host graph) ; the efficiency of resource utilization in an emulation is measured by the expansion of the corresponding embedding (the ratio of the sizes of the host to guest graph). Three main results expose a number of optimal emulations by butterfly networks. Call a family of graphs balanced if complete binary trees can be embedded in the family with simultaneous dilation, congestion, and expansion 0(1). (1) The family of butterfly graphs is balanced. (2) (a) Any graph < from a family of maxdegree-d graphs having a recursive separator of size S(x) can be embedded in any balanced graph family with simultaneous dilation O(log(d Σ i S(2 -i |G|))) and expansion O(1). (b) Any dilation-D embedding of a maxdegree-d graph in a butterfly graph can be converted to an embedding having simultaneous dilation O(D) and congestion O(dD). (3) Any embedding of a planar graph G in a butterfly graph must have dilation Ω(log Σ (G)/Φ(G), where : Σ(G) is the size of the smallest (1/3, 2/3)-node-separator of G, and Φ(G) is the size of G's largest interior face. Applications of these results include : (1) The n-node X-tree network can be emulated by the butterfly network with slowdown O(log log n) and expansion 0(1) ; no embedding has dilation smaller than Ω(log log n), independent of expansion. (2) Every embedding of the n x n mesh in the butterfly graph has dilation Ω(log n) ; any expansion-O(1) embedding in the butterfly graph achieves dilation O(log n). These applications provide the first examples of networks that can be embedded more efficiently in hypercubes than in butterflies. We also show that analogues of these results hold for networks that are structurally related to the butterfly network. The upper bounds hold for the hypercube and the de Bruijn networks, possibly with altered constants. The lower bounds hold-at least in weakened form-for the de Bruijn network.

On the routing of signals in parallel processor meshes

Wormhole message routing is supported by the communication hardware of several distributed memory machines. This particular method of message routing has numerous advantages but creates the problem of a routing deadlock. When long messages compete for the same channels in the network, some messages will be blocked until the first message is fully consumed by the processor at the destination of the message. A deadlock occurs if a set of messages mutually blocks, and no message can progress towards its destination. Most deadlock free routing schemes previously known are designed to work on regular binary hypercubes, a very special case of multicomputer interconnection networks. However, these routing schemes do not provide enough flexibility to deal with the irregular 2-D-tori and attached auxiliary cells found on many newer parallel systems. To handle irregular topologies elegantly, a simple proof is necessary to verify the router code. The new proof given in this report is carried out directly on the network graph. It is constructive in the sense that it reveals the design options to deal with irregularities and shows how additional flexibility can be used to achieve better load balancing. Based on the modified routing model, a set of deadlock free router functions relevant to the iWarp system configurations are described and proven to be correct.

Iterative Dynamic Load Balancing in Multicomputers

Dynamic load balancing in multicomputers can improve the utilization of processors and the efficiency of parallel computations through migrating the workload across processors at runtime. We present a survey and critique of dynamic load balancing strategies that are iterative: that is, workload migration is carried out through transferring processes across nearest neighbour processors. Iterative strategies have become prominent in recent years because of the increaasing popularity of point-to-point interconnection networks for multicomputers.

An approach to emulating separable graphs

A technique foremulating multicomputer interconnection networks that are based onseparable graphs (graphs having bounded degree and sublinear multicolor recursive bisectors) is presented. Efficient emulations among interconnection networks are necessary for porting programs designed for one network to another.

Deadlock-free adaptive routing in multicomputer networks using virtual channels

The use of adaptive routing in a multicomputer interconnection network improves network performance by using all available paths and provides fault tolerance by allowing messages to be routed around failed channels and nodes. Two deadlock-free adaptive routing algorithms are described. Both algorithms allocate virtual channels using a count of the number of dimension reversals a packet has performed to eliminate cycles in resource dependency graphs. The static algorithm eliminates cycles in the network channel dependency graph. The dynamic algorithm improves virtual channel utilization by permitting dependency cycles and instead eliminating cycles in the packet wait-for graph. It is proved that these algorithms are deadlock-free. Experimental measurements of their performance are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>