Set-to-Set Disjoint-Paths Routing in Recursive Dual-Net

Recursive dual-net (RDN) is a newly proposed interconnection network for massive parallel computers. The RDN is based on recursive dual-construction of a symmetric base-network. A k-level dualconstruction for k > 0 creates a network containing (2n0) k /2 nodes with node-degree d0 + k, where n0 and d0 are the number of nodes and the node-degree of the base network, respectively. The RDN is a symmetric graph and can contain huge number of nodes with small node-degree and short diameter. Node-to-set disjoint-paths routing is fundamental and has many applications for fault-tolerant and secure communications in a network. In this paper, we propose an efficient algorithm for set-toset disjoint-paths routing in RDN. We show that, given two sets of d0 + k nodes, S and T in RDN(B), d0 + k disjoint paths, each connecting a node in S to a node in T , can be found in O(lglgN ∗ lgN) time, where N is the number of nodes in RDN(B). The length of the paths is at most 3(D0/2 + 1)(lgN + 1)/(lgn0 + 1), where D0 and n0 are the diameter and the number of nodes of base-network B, respectively.