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Issue No. 01 - January (2009 vol. 20)
ISSN: 1045-9219
pp: 25-33
Iain A. Stewart , University of Durham, Durham
Yonghong Xiang , University of Durham, Durham
In this paper we give precise solutions to problems posed by Wang, An, Pan, Wang and Qu and by Hsieh, Lin and Huang. In particular, we show that Qnk is bipanconnected and edge-bipancyclic, when k ≥ 3 and n ≥ 2, and we also show that when k is odd, Qnk is m-panconnected, for m=(n(k-1)+2k-6)/2, and (k-1)-pancyclic (these bounds are optimal). We introduce a path-shortening technique, called progressive shortening, and strengthen existing results, showing that when paths are formed using progressive shortening then these paths can be efficiently constructed and used to solve a problem relating to the distributed simulation of linear arrays and cycles in a parallel machine whose interconnection network is Qnk, even in the presence of a faulty processor.
Interconnection architectures, Path and circuit problems

I. A. Stewart and Y. Xiang, "Bipanconnectivity and Bipancyclicity in k-ary n-cubes," in IEEE Transactions on Parallel & Distributed Systems, vol. 20, no. , pp. 25-33, 2008.
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