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Paired many-to-many two-disjoint path cover of balanced hypercubes with faulty edges

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Abstract

As a variant of the well-known hypercube, the balanced hypercube \(BH_n\) was proposed as a desired interconnection network topology for parallel computing. It is known that \(BH_n\) is bipartite. Assume that \(S=\{s_1,s_2\}\) and \(T=\{t_1,t_2\}\) are any two sets of vertices in different partite sets of \(BH_n\) (\(n\ge 1\)). It has been proved that there exist two vertex-disjoint \(s_1,t_1\)-path and \(s_2,t_2\)-path of \(BH_n\) covering all vertices of \(BH_n\). In this paper, we prove that there always exist two vertex-disjoint \(s_1,t_1\)-path and \(s_2,t_2\)-path covering all vertices of \(BH_n\) (\(n\ge 2\)) with at most \(2n-3\) faulty edges. The upper bound \(2n-3\) of edge faults can be tolerated is optimal.

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Acknowledgements

The author is grateful to Prof. Simon R. Blackburn for fruitful discussions during his visit to Royal Holloway, University of London. The author would also like to express his gratitude to the anonymous referees for their kind suggestions and comments that greatly improved the original manuscript.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 610054, China

    Huazhong Lü

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  1. Huazhong Lü
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Correspondence to Huazhong Lü.

Additional information

This research was supported by the National Natural Science Foundation of China (No. 11801061) and the Fundamental Research Funds for the Central Universities (No. ZYGX2018J083).

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Lü, H. Paired many-to-many two-disjoint path cover of balanced hypercubes with faulty edges. J Supercomput 75, 400–424 (2019). https://doi.org/10.1007/s11227-018-02734-0

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