Node-to-set disjoint-path routing in perfect hierarchical hypercubes

The perfect hierarchical hypercube structure was proposed in the literature as a topology for interconnection networks of massively parallel systems. It has the useful ability that it can connect many nodes while retaining a low degree as well as a small diameter. In this paper, we introduce an algorithm solving the node-to-set disjoint-path routing problem in a perfect hierarchical hypercube. Inside a (2m + m)-perfect hierarchical hypercube, given one source node and a set of k (≤ m + 1) destination nodes, this algorithm finds k disjoint paths between the source node and all destination nodes of lengths at most m2m + 2m + 2m + 4 in O(km2m) time complexity.