Abstract
Given an edge weighted graph, and an acyclic edge set, the goal of the partial inverse maximum spanning tree problem is to modify the weight function as little as possible such that there exists a maximum spanning tree with respect to the new weight function containing the given edge set. In this paper, we consider this problem with capacitated constraint under the \(l_{p}\)-norm, where p is an integer and \(p \in [1,+\,\infty )\). Firstly, we characterize the feasible solutions of this problem. Then, we present a \(\root p \of {k}\)-approximation algorithm for this problem when the weight function can only be decreased, where k is the number of edges in the given edge set. Finally, when the weight function can be either decreased and increased, we propose an approximation algorithm for the general case and analyse its approximation ratio. Moreover, we remark that these algorithms can be generalized under the weighted \(l_{p}\)-norm and the weighted sum Hamming distance.
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Acknowledgements
This research work is supported in part by National Numerical Windtunnel Project (No. NNW2019ZT5-B16), NSFC (11571155, 11871256, 11771013, 11531011, 61751303), the Fundamental Research Funds for the Central Universities (No. lzujbky-2017-163), and ZJNSFC (LD19A010001).
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Li, X., Zhang, Z., Yang, R. et al. Approximation algorithms for capacitated partial inverse maximum spanning tree problem. J Glob Optim 77, 319–340 (2020). https://doi.org/10.1007/s10898-019-00852-4
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DOI: https://doi.org/10.1007/s10898-019-00852-4