Optimal routing algorithm and the diameter of the cube-connected cycles

Meliksetian, Dikran S.; Chen, C.Y.R.

doi:10.1109/71.246078

Cited by 23 publications

(5 citation statements)

References 6 publications

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“…Many communication algorithms require asymptotically the same time on the cube-connected cycle as on the binary hypercube. Single node broadcastÂgather run in O(log N ) steps, while all other patterns (total exchange, multinode broadcast, and single node scatter) take O(N) steps [210]. Reif and Valiant have given an optimal randomized sorting algorithm on the cube-connected cycle [270], and Leighton has shown how to sort on the butterfly in O(log N ) time on the butterfly with constant queues.…”

Section: Hypercubic and Related Networkmentioning

confidence: 99%

Packet Routing in Fixed-Connection Networks: A Survey

Grammatikakis

Hsu

Kraetzl

et al. 1998

Journal of Parallel and Distributed Computing

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Section: Hypercubic and Related Networkmentioning

confidence: 99%

Packet Routing in Fixed-Connection Networks: A Survey

Grammatikakis

Hsu

Kraetzl

et al. 1998

Journal of Parallel and Distributed Computing

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“…Each node of a ring is connected in one dimension of the Hypercube. The degree is constant and equal to 3 [3]. The definition of CCC can be generalized to different lengths of cycles of the size of the cube.…”

Section: The Cube Connected Cycle CCC Topologymentioning

confidence: 99%

“…(3,2) de bruijn graph where d = 3 and k = 2. This graph represents 3 2 nodes • Various de Bruijn networks:…”

mentioning

confidence: 99%

A Heuristic (delta, D) Digraph to Interpolate between Hypercube and de Bruijn Topologies for Future On-Chip Interconnection Networks

Damaj

Goubier

Blanc

et al. 2009

2009 International Conference on Parallel Processing Workshops

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The paper presents as background several graphs referred to (delta, D) digraphs including the Hypercube and de Bruijn. It shows the major disadvantages when implementing these topologies on chip interconnection networks. Then, the paper presents the "Small-World Heuristic" (SWH), which aims to find a network topology for a large number of nodes that has a maximum out degree and a small diameter, while maintaining an acceptable level of connectivity. It is proposed that this heuristic can be used to determine a compromise between Hypercube and de Bruijn when implementing networks on FPGA or in VLSI.

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“…It is instructive to compare the diameter Qg À Q, derived above, with the diameter PXSg À P of a CCC network of the same size [21]. The slightly larger diameter of the PRC ring is due to the unidirectional links and lower node degree (CCC has node in/out-degree of 3).…”

Section: Proofmentioning

confidence: 99%

Periodically regular chordal rings

Parhami

Kwai

1999

IEEE Trans. Parallel Distrib. Syst.

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AbstractÐChordal rings have been proposed in the past as networks that combine the simple routing framework of rings with the lower diameter, wider bisection, and higher resilience of other architectures. Virtually all proposed chordal ring networks are nodesymmetric, i.e., all nodes have the same in/out degree and interconnection pattern. Unfortunately, such regular chordal rings are not scalable. In this paper, periodically regular chordal (PRC) ring networks are proposed as a compromise for combining low node degree with small diameter. By varying the PRC ring parameters, one can obtain architectures with significantly different characteristics (e.g., from linear to logarithmic diameter), while maintaining an elegant framework for computation and communication. In particular, a very simple and efficient routing algorithm works for the entire spectrum of PRC rings thus obtained. This flexibility has important implications for key system attributes such as architectural scalability, software portability, and fault tolerance. Our discussion is centered on unidirectional PRC rings with in/out-degree of 2. We explore the basic structure, topological properties, optimization of parameters, VLSI layout, and scalability of such networks, develop packet and wormhole routing algorithms for them, and briefly compare them to competing fixed-degree architectures such as symmetric chordal rings, meshes, tori, and cube-connected cycles.

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Optimal routing algorithm and the diameter of the cube-connected cycles

Cited by 23 publications

References 6 publications

Packet Routing in Fixed-Connection Networks: A Survey

Packet Routing in Fixed-Connection Networks: A Survey

A Heuristic (delta, D) Digraph to Interpolate between Hypercube and de Bruijn Topologies for Future On-Chip Interconnection Networks

Periodically regular chordal rings

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