Abstract
This paper studies a spanning tree problem with interval data that finds diverse applications in network design. Given an underlying network G = (V,E), each link e ∈ E can be established by paying a cost \(c_e\in[\underline{c}_e,\overline{c}_e]\), and accordingly takes a risk \(\frac{\overline{c}_e-c_e}{\overline{c}_e-\underline{c}_e}\) of link failure. The minimum risk spanning tree (MRST) problem is to establish a spanning tree in G of total cost no more than a given constant so that the risk sum over the links on the spanning tree is minimized. In this paper, we propose an exact algorithm for the MRST problem that has time-complexity of O(m 2logm logn(m + n logn)), where m = |E| and n = |V|.
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Chen, X., Hu, J., Hu, X. (2007). The Minimum Risk Spanning Tree Problem. In: Dress, A., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2007. Lecture Notes in Computer Science, vol 4616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73556-4_11
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DOI: https://doi.org/10.1007/978-3-540-73556-4_11
Publisher Name: Springer, Berlin, Heidelberg
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