Set-to-Set Disjoint Paths Routing in Hierarchical Cubic Networks

Due to its simplicity, the hypercube topology is popular as interconnection network of parallel systems. However, due to physical restrictions of the number of links per node, this topology is no more satisfactory in the context of modern supercomputing. Effectively, today massively parallel systems, such as the Fujitsu K computer, connect hundreds of thousands of nodes (705 024 nodes for the K, connected according to a six-dimensional torus network). Focusing on degree reduction, a variation of the hypercube topology called hierarchical cubic networks (HCNs) was described. An HCN contains almost half of the number of edges of an hypercube of the same size, and additionally, its diameter is also smaller. We describe in this paper a set-to-set disjoint paths routing algorithm in an HCN (n), finding between two disjoint sets of nodes at most n+1 mutually node-disjoint paths of lengths at most 6n+3 in O(n(2)log n) time.