Issue No. 09 - September (1996 vol. 45)

ISSN: 0018-9340

pp: 1056-1062

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.537129

ABSTRACT

<p><b>Abstract</b>—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 <it>d</it> and dimension <it>n</it>, denoted by <it>UB</it>(<it>d, n</it>). We first discuss the shortest-path routing problem. We present properties of the shortest paths between any two vertices of <it>UB</it>(<it>d, n</it>) 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 <it>UB</it>(<it>d, n</it>) when <it>d</it>≥ 5. We present a transmitting scheme on undirected binary de Bruijn networks <it>UB</it>(2, <it>n</it>) with transmitting time <it>n</it>− 1 for <it>n</it>≥ 5, and conjecture that the optimal transmitting time is <it>n</it>− 1 for <it>UB</it>(2, <it>n</it>), and <it>n</it> for <it>UB</it>(3, <it>n</it>) and <it>UB</it>(4, <it>n</it>).</p>

INDEX TERMS

Interconnection networks, de Bruijn networks, shortest paths, string matching, prefix trees, transmitting.

CITATION

Zhen Liu, Ting-Yi Sung, "Routing and Transmitting Problems in de Bruijn Networks",

*IEEE Transactions on Computers*, vol. 45, no. , pp. 1056-1062, September 1996, doi:10.1109/12.537129