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<p><b>Abstract</b>—A combined (2<it>log</it>N − 1)-stage interconnection network (denoted by <tmath>$\Delta \oplus \Delta '$</tmath>) 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<it>log</it>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 <tmath>$\Delta \oplus \Delta '$</tmath> networks is very limited so far. In this paper, we study the topological structure of <tmath>$\Delta \oplus \Delta '$</tmath> networks and propose an algorithm for determining topological equivalence between two given <tmath>$\Delta \oplus \Delta '$</tmath> networks. We also present a simplified Ω-equivalence checking algorithm as a supporting result.</p>
Combined (2logN − 1)-stage network, equivalence, multistage interconnection network, permutation, topology, Ω-equivalent class
Jingyu Yang, Xiaojun Shen, Qing Hu, "Topologies of Combined (2logN - 1)-Stage Interconnection Networks", IEEE Transactions on Computers, vol. 46, no. , pp. 118-124, January 1997, doi:10.1109/12.559812
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