Efficient Collective Communications in Dual-Cube

Li, Yamin; Peng, Shietung; Chu, Wanming

doi:10.1023/b:supe.0000014803.83151.dc

Cited by 70 publications

(37 citation statements)

References 19 publications

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“…Table 2 lists the topological properties of the torus, n-cube, CCC [9], DualCube [6], RDN, and HDN. The CCC (cube-connected cycles) is obtained by replacing a node in an n-cube with an n-node cycle.…”

Section: Theorem 1 Assume That the Base Network B Is A Symmetric Prmentioning

confidence: 99%

Total Exchange Routing on Hierarchical Dual-Nets

Chu

2013

Lecture Notes in Computer Science

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Abstract. The hierarchical dual-net (HDN) is a newly proposed interconnection network for massive parallel computers. The HDN is constructed based on a symmetric product graph (base network).is a super-node and si = |G i | is the number of nodes in the super-node at the level i for 1 ≤ i ≤ k, and n0 is the number of nodes in the base network B. The S is used mainly for adjusting the scale of the system. The node degree of HDN(B, k, S) is d0 + k, where d0 is the node degree of the base network. The HDN is node and edge symmetric and can contain huge number of nodes with small node-degree and short diameter. The total exchange is one of the most dense communication patterns and is at the heart of numerous applications and programming models in parallel computing. In this paper, we show that the total exchange routing can be done on HDN efficiently.

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Section: Theorem 1 Assume That the Base Network B Is A Symmetric Prmentioning

confidence: 99%

Total Exchange Routing on Hierarchical Dual-Nets

Chu

2013

Lecture Notes in Computer Science

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“…However, a state-of-the-art massively parallel system interconnects tens of thousands of nodes, so new topologies are necessary. In this study, we focus on such a topology, dual-cube [1]. The dual-cube is an extension of the hypercube [2], and it addresses some of the drawbacks of the hypercube when applied to massively parallel systems.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Fault-Tolerant Routing in Dual-Cubes

Park

Seki

Kaneko

2017

IEICE Trans. Inf. & Syst.

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SUMMARYIn the topologies for interconnected nodes, it is desirable to have a low degree and a small diameter. For the same number of nodes, a dual-cube topology has almost half the degree compared to a hypercube while increasing the diameter by just one. Hence, it is a promising topology for interconnection networks of massively parallel systems. We propose here a stochastic fault-tolerant routing algorithm to find a non-faulty path from a source node to a destination node in a dual-cube.

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“…Not only are hypercubes popular as interconnection network on their own, but they are also very popular as seed for advanced network topologies such as those employed by hierarchical interconnection networks (HINs). Hierarchical hypercubes [4,5,6,7], hierarchical cubic networks [8,9,10], metacubes [11,12], dual-cubes [13,14] are some examples.…”

Section: Introductionmentioning

confidence: 99%

Hypercube Fault Tolerant Routing with Bit Constraint

Bossard

Kaneko

2015

IJNC

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Thanks to its simple definition, the hypercube topology is very popular as interconnection network of parallel systems. There have been several routing algorithms described for the hypercube topology, yet in this paper we focus on hypercube routing extended with an additional restriction: bit constraint. Concretely, path selection is performed on a particular subset of nodes: the nodes are required to satisfy a condition regarding their bit weights (a.k.a. Hamming weights). There are several applications to such restricted routing, including simplification of disjoint paths routing. We propose in this paper two hypercube routing algorithms enforcing such node restriction: first, a shortest path routing algorithm, second a fault tolerant point-topoint routing algorithm. Formal proof of correctness and complexity analysis for the described algorithms are conducted. We show that the shortest path routing algorithm proposed is time optimal. Finally, we perform an empirical evaluation of the proposed fault tolerant point-topoint routing algorithm so as to inspect its practical behaviour. Along with this experimentation, we analyse further the average performance of the proposed algorithm by discussing the average Hamming distance in a hypercube when satisfying a bit constraint.

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Efficient Collective Communications in Dual-Cube

Cited by 70 publications

References 19 publications

Total Exchange Routing on Hierarchical Dual-Nets

Total Exchange Routing on Hierarchical Dual-Nets

Stochastic Fault-Tolerant Routing in Dual-Cubes

Hypercube Fault Tolerant Routing with Bit Constraint

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