k-pairwise disjoint paths routing in perfect hierarchical hypercubes

  • Authors:

  • Antoine Bossard;Keiichi Kaneko

  • Affiliations:

  • Graduate School of Engineering, Tokyo University of Agriculture and Technology, Tokyo, Japan;Graduate School of Engineering, Tokyo University of Agriculture and Technology, Tokyo, Japan

  • Venue:
  • The Journal of Supercomputing
  • Year:
  • 2014

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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 (2m+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=驴(m+1)/2驴 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 2m+1+m(2m+1+1)+4 in O(25m) time, where 2m+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.