Interconnection Networks Of Parallel Systems Research Articles

Set-to-set disjoint paths in a folded hypercube

The hypercube is a very popular topology for the interconnection networks of parallel systems, and the folded hypercube is a variant of the hypercube. The folded hypercube attains much higher performance by introducing one additional link to each processing element. Therefore, there are many research activities regarding the folded hypercube. We focus on this topology and address an unresolved problem, that is, the set-to-set disjoint paths problem in it. In this paper, we show an algorithm that solves the problem in a folded hypercube in polynomial time. We prove the correctness of the algorithm. Moreover, we show that the time complexity of the algorithm is O(ν3log⁡ν) and the maximum length of the paths is 2ν+2 if the algorithm is applied to a ν-dimensional folded hypercube.

Fractional Matching Preclusion for Restricted Hypercube-Like Graphs

The restricted hypercube-like graphs, variants of the hypercube, were proposed as desired interconnection networks of parallel systems. The matching preclusion number of a graph is the minimum number of edges whose deletion results in the graph with neither perfect matchings nor almost perfect matchings. The fractional perfect matching preclusion and fractional strong perfect matching preclusion are generalizations of the matching preclusion. In this paper, we obtain fractional matching preclusion number and fractional strong matching preclusion number of restricted hypercube-like graphs, which extend some known results.

Performance-aware Energy Saving Mechanism in Interconnection Networks for Parallel Systems

The growing processing power of parallel computing systems require interconnection networks a higher level of complexity and higher performance, thus consuming more energy. Link components contributes a substantial proportion of the total energy consumption of the networks. Many researchers have proposed approaches to judiciously change the link speed as a function of traffic to save energy when the traffic is light. However, the link speed reduction incurs an increase in average packet latency, thus degrades network performance. This paper addresses that issue with a performance-aware energy saving mechanism. The simulation results show that the proposed mechanism outperforms the energy saving mechanisms in literature.

The Folded Crossed Cube : A New Interconnection Network For Parallel Systems

of parallel computer interconnection network topology has been made along with the various interconnection networks emphasizing the cube based topologies in particular. This paper proposes a new cube based topology called the Folded crossed cube with better features such as reduced diameter, cost and improved broadcast time, better fault tolerance and better message traffic density in comparison to its parent topologies: viz: hypercube and crossed cube. The one-to-one routing algorithm is also designed for the proposed network. The topological properties along with routing time are compared with the parent topologies and found to be better. Performance analysis in terms of cost, reliability is also done for the current network.

Eligibility-based round robin for fair and efficient packet scheduling in wormhole switching networks

Interconnection networks of parallel systems are used for servicing traffic generated by different applications, often belonging to different users. When multiple users contend for channel bandwidth, fairness in bandwidth sharing becomes a key requirement. In fact, enforcing a fair sharing of channel bandwidth improves flow isolation, thus preventing misbehaving flows from affecting the performance of other flows. We present a novel packet scheduling algorithm, called eligibility-based round robin (EBRR), devised to provide fair queueing in interconnection networks. In fact, EBRR meets the constraints imposed by wormhole switching, which is the most popular switching technique in interconnection networks of parallel systems. It can also be applied to packet switching wide area networks (WANs), such as IP and ATM. We show that EBRR has O(1) complexity and better delay and fairness properties than existing algorithms of comparable complexity. Here, we also investigate the means for assessing the fairness of a scheduler: we show that using the relative fairness bound as a fairness measure may lead to erroneous results. We then propose an alternative measure, called the generalized relative fairness bound, that allows fairness to be assessed more precisely.

Anchored opportunity queueing: a low-latency scheduler for fair arbitration among virtual channels

Many wormhole interconnection networks for parallel systems, and more recently system area networks, implement virtual channels to provide a number of services including improved link utilization and lower latencies. The forwarding of flits from the virtual channels on to the physical channel is typically accomplished using flit-based round-robin (FBRR) scheduling. This paper presents a novel scheduling strategy, anchored opportunity queueing ( AOQ), which preserves the throughput and fairness characteristics of FBRR while significantly reducing the average delay experienced by packets. The AOQ scheduler achieves lower average latencies by trying, as far as possible, to complete the transmission of a complete packet before beginning the transmission of flits from another packet. The AOQ scheduler achieves provable fairness in the number of opportunities it offers to each of the virtual channels for transmissions of flits over the physical channel. We prove this by showing that the relative fairness bound, a popular measure of fairness, is a small finite constant in the case of the AOQ scheduler. Finally, we present simulation results comparing the delay characteristics of AOQ with other schedulers for virtual channels. The AOQ scheduler is simple to implement in hardware, and also offers a practical solution in other contexts such as in scheduling ATM cells in Internet backbone switches.

A new injection limitation mechanism for wormhole networks

Wormhole switching has been widely applied to the interconnection networks of parallel systems as well as System Area Networks, and Local Area Networks, largely because of its efficiency and performance merits. Examples include the Myrinet of Myricom Inc as well as most of the newly developed parallel systems. True Fully Adaptive Routing (TFAR) Algorithms have demonstrated their suitability for wormhole switched networks due to their unrestricted Adaptivity and moderate resource requirements. Wormhole switching has proven to be the most popular switching technique targeted for interconnection networks of message-passing multicomputers as well as SANs, and LANs. TFAR Algorithms have also been gaining favor for application in wormhole switched networks due to their highly adaptive and moderate hardware requirements. Wormhole switched networks have associated drawbacks however, as they generally suffer from performance degradation beyond the saturation point due to channel congestion. Fully adaptive algorithms are vulnerable to cyclic dependencies, which are precursors to deadlock formations. Consequently the frequent occurrence of deadlocks can further degrade the performance and stability characteristics of these networks. Injection limitation techniques were recently introduced in an attempt to countermeasure these drawbacks and effectively contain their impact on the performance of the network. This paper proposes a new injection limitation mechanism and its performance evaluation. The new mechanism is named Congestion Level Injection Control (CLIC). This mechanism attempts to provide a solution for these problems and improve the overall performance of the network. The new mechanism is centered on congestion level estimation in the network using only local information at each node. The mechanism subsequently prevents the injection of new packets if the network is deemed to be highly congested or possibly close to its saturation point. The performance of the CLIC mechanism has been compared with other competing schemes. Our results have shown that CLIC has superior performance when compared to other competing schemes.

Decomposable trees: a polynomial algorithm for tripodes

In this article, we deal with graphs modelling interconnection networks of parallel systems (parallel computers, networks of workstations, etc.). We want to share the nodes of such a network between many users, each one needing a given number of nodes. Thus, a graph G with N vertices is said to be decomposable if for each set { n 1,…, n k } whose sum is equal to N, there exists a partition V 1,…, V k of V( G) such that for each i, 1⩽ i⩽ k, | V i |= n i and the subgraph induced by V i is connected. We show that determining whether a given tripode (three disjoint chains connected by one extremity to a same new vertex) is decomposable can be done by a polynomial algorithm.

Fair and efficient packet scheduling using Elastic Round Robin

Parallel systems are increasingly being used in multiuser environments with the interconnection network shared by several users at the same time. Fairness is an intuitively desirable property in the allocation of bandwidth available on a link among traffic flows of different users that share the link. Strict fairness in traffic scheduling can improve the isolation between users, offer a more predictable performance and improve performance by eliminating some bottlenecks. This paper presents a simple, fair, efficient, and easily implementable scheduling discipline, called Elastic Round Robin (ERR), designed to satisfy the unique needs of wormhole switching, which is popular in interconnection networks of parallel systems. In spite of the constraints of wormhole switching imposed on the design, ERR is also suitable for use in Internet routers and has better fairness and performance characteristics than previously known scheduling algorithms of comparable efficiency, including Deficit Round Robin and Surplus Round Robin. In this paper, we prove that ERR is efficient, with a per-packet work complexity of O(1). We analytically derive the relative fairness bound of ERR, a popular metric used to measure fairness. We also derive the bound on the start-up latency experienced by a new flow that arrives at an ERR scheduler. Finally, this paper presents simulation results comparing the fairness and performance characteristics of ERR with other scheduling disciplines of comparable efficiency.

Uniform emulations of Cartesian-product and Cayley graphs

In this paper, we consider graphs modeling interconnection networks of parallel systems and we deal with network simulations. More specifically, we focus on simulations involving Cartesian-product graphs and some subclasses of Cayley graphs. We study emulations based on graph homomorphisms and iso-retractions. In particular, we give necessary and sufficient conditions for the existence of an iso-retraction of a Cartesian product graph G□H onto graph G. Furthermore, we show that each uniform (in terms of the load of the vertices in the target graph) emulation of the hypercube Hn onto the hypercube Hn−1 is an iso-retraction. Finally, we deal with iso-retractions of transposition Cayley graphs.