Mutually independent Hamiltonian cycles in dual-cubes

Shih, Yuan-Kang; Chuang, Hui-Chun; Kao, Shin-Shin; Tan, Jinglu

doi:10.1007/s11227-009-0317-2

Cited by 19 publications

(4 citation statements)

References 26 publications

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“…In particular, hierarchical interconnection networks (HINs) have proven very popular. Amongst those, dual-cubes (Li et al, 2004) are actively researched: as examples, Zhou et al (2012a) discussed dual-cube conditional fault diagnosability, and Shih et al (2010) give a constructive proof of the existence of Hamiltonian cycles in dual-cubes.…”

Section: State Of the Artmentioning

confidence: 99%

Torus–Connected Cycles: A Simple and Scalable Topology for Interconnection Networks

Bossard

Kaneko

2015

International Journal of Applied Mathematics and Computer Science

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Supercomputers are today made up of hundreds of thousands of nodes. The interconnection network is responsible for connecting all these nodes to each other. Different interconnection networks have been proposed; high performance topologies have been introduced as a replacement for the conventional topologies of recent decades. A high order, a low degree and a small diameter are the usual properties aimed for by such topologies. However, this is not sufficient to lead to actual hardware implementations. Network scalability and topology simplicity are two critical parameters, and they are two of the reasons why modern supercomputers are often based on torus interconnection networks (e.g., Fujitsu K, IBM Sequoia). In this paper we first describe a new topology, torus-connected cycles (TCCs), realizing a combination of a torus and a ring, thus retaining interesting properties of torus networks in addition to those of hierarchical interconnection networks (HINs). Then, we formally establish the diameter of a TCC, and deduce a point-to-point routing algorithm. Next, we propose routing algorithms solving the Hamiltonian cycle problem, and, in a two dimensional TCC, the Hamiltonian path one. Correctness and complexities are formally proved. The proposed algorithms are time-optimal.

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Section: State Of the Artmentioning

confidence: 99%

Torus–Connected Cycles: A Simple and Scalable Topology for Interconnection Networks

Bossard

Kaneko

2015

International Journal of Applied Mathematics and Computer Science

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“…Lai and Tsai [26] obtained the vertex bipancyclicity of dual-cube, and showed that dual-cube is bipancyclic even if it has up to n − 1 faulty edges. Shih et al [41] proved the existence of n + 1 mutually independent hamiltonian cycles in dual-cube. Let S 2 be the symmetric group of order 2, and Z 2 be the cyclic group of order 2.…”

Section: Definition 2 [8]mentioning

confidence: 99%

Conditional Fault Diagnosability of Dual-Cubes

Zhou

Chen

2012

Int. J. Found. Comput. Sci.

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The growing size of the multiprocessor system increases its vulnerability to component failures. It is crucial to locate and replace the faulty processors to maintain a system's high reliability. The fault diagnosis is the process of identifying faulty processors in a system through testing. This paper shows that the largest connected component of the survival graph contains almost all of the remaining vertices in the dual-cube DCn when the number of faulty vertices is up to twice or three times of the traditional connectivity. Based on this fault resiliency, this paper determines that the conditional diagnosability of DCn (n ≥ 3) under the comparison model is 3n − 2, which is about three times of the traditional diagnosability.

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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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Mutually independent Hamiltonian cycles in dual-cubes

Cited by 19 publications

References 26 publications

Torus–Connected Cycles: A Simple and Scalable Topology for Interconnection Networks

Torus–Connected Cycles: A Simple and Scalable Topology for Interconnection Networks

Conditional Fault Diagnosability of Dual-Cubes

Hypercube Fault Tolerant Routing with Bit Constraint

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