Fault-tolerant routing and disjoint paths in dual-cube: a new interconnection network

In this paper, we introduce a new interconnection network, the dual-cube, its topological properties, and the routing/broadcasting algorithms in the dual-cube. The advanced subjects such as fault-tolerant routing and constructing multiple disjoint paths in dual-cubes are also included in this paper. The binary hypercube, or r-cube, can connect 2^r nodes. In contrast, a dual-cube with r links for each node, F_r, can connect 2^2r-1 nodes while keeps most of topological properties of hypercubes. Fault-tolerant routing and constructing multiple disjoint paths in dual-cubes can be solved elegantly using a new structure, called extended cube. We show that for any two nonfaulty nodes s and t in F_r which contains up to r-1 faulty nodes, we can find a fault-free path s to t, of length at most 3d(s,t) in O(r) optimal time, where d(s,t) is the distance between s and t. We also show that, in a fault-free F_r, r disjoint paths s to t, of length at most d(s,t)+6 can be constructed in O(r²) optimal time