Abstract
Constructing vertex-disjoint spanning trees (VDSTs for short) of a given network is an important issue in the research of network fault-tolerance and security. The star network was proposed as an attractive interconnection network model for competing with n-cube. Accordingly, Rescigno in [Inform. Sci. 137 (2001) 259–276] proposed an algorithm to construct \(n-1\) VDSTs rooted at a common node in an n-dimensional star network \(S_n\). In this paper, we point out that there exists a flaw in Rescigno’s algorithm, and thus the spanning trees constructed by this algorithm may not be vertex-disjoint. As a result, a correct scheme of constructing \(n-1\) VDSTs on \(S_n\) is presented. Moreover, based on the reversing rule of building certain paths of VDSTs in the amendatory scheme, we propose a new algorithm to construct \(n-1\) VDSTs with optimal heights on \(S_n\). In particular, the proposed algorithm is more efficient and can easily be implemented in parallel.
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Acknowledgments
This research was partially supported by MOST grants 104-2221-E-141-002-MY3 (Jou-Ming Chang), 105-2221-E-131-027 (Kung-Jui Pai), 106-2221-E-141-001 (Jinn-Shyong Yang) and 104-2221-E-262-005 (Ro-Yu Wu) from the Ministry of Science and Technology, Taiwan.
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Kao, SS., Chang, JM., Pai, KJ., Yang, JS., Tang, SM., Wu, RY. (2017). A Parallel Construction of Vertex-Disjoint Spanning Trees with Optimal Heights in Star Networks. In: Gao, X., Du, H., Han, M. (eds) Combinatorial Optimization and Applications. COCOA 2017. Lecture Notes in Computer Science(), vol 10627. Springer, Cham. https://doi.org/10.1007/978-3-319-71150-8_4
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DOI: https://doi.org/10.1007/978-3-319-71150-8_4
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