Disjoint-Path Routing on Hierarchical Dual-Nets

The hierarchical dual-net (HDN) was introduced as a topology of interconnection networks for extremely large parallel computers. The HDN is constructed based on a symmetric product graph (base network). A k-level hierarchical dual-net, HDN(B,k,S), contains (2N₀)^2k/(2 × Π_i=1^k s_i) nodes, where S = {G'₁, G'₂, . . . , G'_k}, G'_i is a super-node and s_i = |G'_i| is the number of nodes in the super-node at the level i for 1 ≤ i ≤ k, and N₀ is the number of nodes in the base network B. The node degree of HDN(B, k, S) is d₀ + k, where d₀ is the node degree of the base network. The HDN is node and edge symmetric and can contain huge number of nodes with small node-degree and short diameter. Disjoint-path routing is a fundamental and critical issue for the performance of an interconnection network. In this paper, we propose an efficient algorithm for finding disjoint-paths on an HDN and give the performance simulation results.