Topologies of combined (2 log N-1)-stage interconnection networks

A combined (2 log N-1)-stage interconnection network (denoted by Δ⊕Δ´) is constructed by concatenating two Omega-equivalent networks (Δ and Δ´) with the rightmost stage of Δ and the leftmost stage of Δ´ overlapped. Benes network and the (2 log N-1)-stage shuffle-exchange network are two examples of such networks. Although these two networks have received intensive studies, the research on the topology of entire class of Δ⊕Δ´ networks is very limited so far. In this paper, we study the topological structure of Δ⊕Δ´ networks and propose an algorithm for determining topological equivalence between two given Δ⊕Δ´ networks. We also present a simplified Ω-equivalence checking algorithm as a supporting result