Set-to-set disjoint paths in a folded hypercube

Abstract

The hypercube is a very popular topology for the interconnection networks of parallel systems, and the folded hypercube is a variant of the hypercube. The folded hypercube attains much higher performance by introducing one additional link to each processing element. Therefore, there are many research activities regarding the folded hypercube. We focus on this topology and address an unresolved problem, that is, the set-to-set disjoint paths problem in it. In this paper, we show an algorithm that solves the problem in a folded hypercube in polynomial time. We prove the correctness of the algorithm. Moreover, we show that the time complexity of the algorithm is O(ν3log⁡ν) and the maximum length of the paths is 2ν+2 if the algorithm is applied to a ν-dimensional folded hypercube.