Banyan networks for partitioning multiprocessor systems

Goke, L. Rodney; Lipovski, G. Jack

doi:10.1145/285930.285972

Cited by 284 publications

(23 citation statements)

References 7 publications

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“…Banyan networks were first introduced by Goke and Lipovski [6] using graph methods. In a simplifying approach, any multistage network for which there is a unique path from each network input to each network output is called a banyan network.…”

Section: Realizing Semi-permutations In a Banyan Networkmentioning

confidence: 99%

“…A MIN can be blocking such as a banyan network [6], rearrangeably nonblocking such as a Benes network [1], nonblocking such as crossbar [15], or with variable connecting capabilities, from rearrangeable for permutation to nonblocking for multicast, such as a Clos network [1], [4], [19], depending on the number of stages, the number of switches, the switch capability, and the interconnection patterns used between stages. MINs have been extensively studied in the literature, e.g., see [1], [6], [4], [18], [19]. However, most of the research reported are for electronic MINs.…”

Section: Introductionmentioning

confidence: 99%

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Permutation capability of optical multistage interconnection networks

Yang

Wang²,

Pan

Proceedings of the First Merged International Parallel Processing Symposium and Symposium on Parallel and Distributed Processin

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In this paper, we study optical multistage interconnection networks (MINs). Advances in electro-optic technologies have made optical communication a promising networking choice to meet the increasing demands for high channel bandwidth and low communication latency of high-performance computing/communication applications. Although optical MINs hold great promise and have demonstrated advantages over their electronic counterpart, they also hold their own challenges. Due to the unique properties of optics, crosstalk in optical switches should be avoided to make them work properly. Most of the research work described in the literature are for electronic MINs, and hence, crosstalk is not considered. In this paper, we introduce a new concept, semipermutation, to analyze the permutation capability of optical MINs under the constraint of avoiding crosstalk, and apply it to two examples of optical MINs, banyan network and Benes network. For the blocking banyan network, we show that not all semi-permutations are realizable in one pass, and give the number of realizable semi-permutations. For the rearrangeable Benes network, we show that any semi-permutation is realizable in one pass and any permutation is realizable in two passes under the constraint of avoiding crosstalk. A routing algorithmfor realizing a semi-permutation in a Benes network is also presented. With the speed and bandwidthprovided by current optical technology, an optical MIN clearly demonstrates a superior overall performance over its electronic MIN counterpart.

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Section: Realizing Semi-permutations In a Banyan Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Permutation capability of optical multistage interconnection networks

Yang

Wang²,

Pan

Proceedings of the First Merged International Parallel Processing Symposium and Symposium on Parallel and Distributed Processin

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“…Since K=4 and log 2 K=2, so we need two levels decompositions to decompose the permutation into K = 4 CRPPs for the VSB (16,4) network. First-level decomposition: Take the permutation (4) as the 0-level partial permutation.…”

Section: Fig3 Recursive Definition Of An N× × × ×N Benes Networkmentioning

confidence: 99%

“…Available optical MINs were built mainly on banyan [4] or its equivalent (e.g. baseline, omega) networks [5,6] because they are fast in switch setting (self-routing) and also have a small number of switches between an input-output pair, see for example [3,7,8,9,12].…”

Section: Introductionmentioning

confidence: 99%

Vertically stacked Benes networks for crosstalk-free permutation

Jiang

Shen

Khandker

et al.

First International Symposium on Cyber Worlds, 2002. Proceedings.

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Crosstalk in optical switching elements (SEs) is one of the major shortcomings in optical switching networks, and avoiding crosstalk is an important issue for making optical network work properly. We propose a new class of optical multistage interconnection networks (MINs)vertically stacked Benes network VSB(N, K) that has N inputs (outputs) and consists of K vertically stacked Benes network. The VSB(N, K) network can support any permutation of N-element set {0,1,…,N-1} rearrangeablynonblocking and also free of first-order crosstalk in SEs with a higher flexibility and much lower hardware cost than that of available optical MINs built on a combination of horizontal expansion and vertical stacking of Banyan networks. The complete algorithms to realize permutation crosstalk-free in a VSB (N, K) network are also the main contributions of this paper.

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“…Banyan networks [3], originally designed as switching networks for shared-memory multiprocessors, can also be adopted for distributed-memory processor networks. In that case, each node of a banyan network is a processor.…”

Section: Introductionmentioning

confidence: 99%

Hyperbanyan networks: a new class of networks for distributed-memory multiprocessors

Ferner

Lee

[Proceedings 1992] the Fourth Symposium on the Frontiers of Massively Parallel Computation

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In this paper, a new class of connection topologies for distributed-memory multiprocessors, Hyperbanyan Networks, is introduced. A Hyperbanyan is a combination of the t o ological designs of a banyan [3] and the Hypertree [dfnetworks. Since the Hyperfree combines the advantages of the binary tree and the hypercube, a Hyperban.yan, has the features of a binary tree, a hypercube, as well as a banyan.The Hyperbanyans have a fixed degree of 5 and the diameter of an (n stage x 2"-' nodes/stage) Hyperbanyan is 2(n -1). A rou2in.g algorithm wh,ich is close t o optimal is presented. 254 0-8186-2'l72-1/92 $3.00 0 1992 IEEE

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Banyan networks for partitioning multiprocessor systems

Cited by 284 publications

References 7 publications

Permutation capability of optical multistage interconnection networks

Permutation capability of optical multistage interconnection networks

Vertically stacked Benes networks for crosstalk-free permutation

Hyperbanyan networks: a new class of networks for distributed-memory multiprocessors

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