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Routing and Transmitting Problems in de Bruijn Networks
September 1996 (vol. 45 no. 9)
pp. 1056-1062

Abstract—De Bruijn graphs, both directed and undirected, have received considerable attention as architecture for interconnection networks. In this paper, we focus on undirected de Bruijn networks of radix d and dimension n, denoted by UB(d, n). We first discuss the shortest-path routing problem. We present properties of the shortest paths between any two vertices of UB(d, n) and propose two shortest-path routing algorithms, one of which has linear time complexity. Secondly, we study the transmitting problem. We establish a lower bound for the optimal transmitting time which implies in particular that the optimal transmitting problem is trivial for UB(d, n) when d≥ 5. We present a transmitting scheme on undirected binary de Bruijn networks UB(2, n) with transmitting time n− 1 for n≥ 5, and conjecture that the optimal transmitting time is n− 1 for UB(2, n), and n for UB(3, n) and UB(4, n).

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Index Terms:
Interconnection networks, de Bruijn networks, shortest paths, string matching, prefix trees, transmitting.
Zhen Liu, Ting-Yi Sung, "Routing and Transmitting Problems in de Bruijn Networks," IEEE Transactions on Computers, vol. 45, no. 9, pp. 1056-1062, Sept. 1996, doi:10.1109/12.537129
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