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The Journal of Supercomputing

, Volume 67, Issue 2, pp 485–495 | Cite as

k-pairwise disjoint paths routing in perfect hierarchical hypercubes

  • Antoine BossardEmail author
  • Keiichi Kaneko
Article

Abstract

Hierarchical hypercubes (HHC), also known as cube-connected cubes, have been introduced in the literature as an interconnection network for massively parallel systems. Effectively, they can connect a large number of nodes while retaining a small diameter and a low degree compared to a hypercube of the same size. Especially (2 m +m)-dimensional hierarchical hypercubes (\(\mathit {HHC}_{2^{m}+m}\)), called perfect HHCs, are popular as they are symmetrical, which is a critical property when designing routing algorithms. In this paper, we describe an algorithm finding, in an \(\mathit{HHC}_{2^{m}+m}\), mutually node-disjoint paths connecting k=⌈(m+1)/2⌉ pairs of distinct nodes. This problem is known as the k-pairwise disjoint-path routing problem and is one of the important routing problems when dealing with interconnection networks. In an \(\mathit{HHC}_{2^{m}+m}\), our algorithm finds paths of lengths at most 2 m+1+m(2 m+1+1)+4 in O(25m ) time, where 2 m+1 is the diameter of an \(\mathit{HHC}_{2^{m}+m}\). Also, we have shown through an experiment that, in practice, the lengths of the generated paths are significantly lower than the worst-case theoretical estimations.

Keywords

Interconnection network Algorithm Parallel processing Supercomputer HHC 

Notes

Acknowledgements

The authors sincerely thank the reviewers, especially Reviewers 1, 2, 4, 5, 6, and 9, for their insightful comments and suggestions that greatly improved the quality of this paper.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Graduate School of EngineeringTokyo University of Agriculture and TechnologyTokyoJapan

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