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Partial Inverse Min-Max Spanning Tree Problem Under the Weighted Bottleneck Hamming Distance

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Algorithmic Aspects in Information and Management (AAIM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13513))

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Abstract

Given a undirected connected weighted graph G and a forest F of G, the partial inverse min-max spanning tree problem is to adjust weight function with minimum cost such that there is a min-max spanning tree with respect to the new weight function containing F. In this paper, we study this problem under the weighted bottleneck Hamming distance. Firstly, we consider this problem with value of optimal tree restriction, and present a polynomial time algorithm to solve it. Then, by characterizing the properties of the value of optimal tree, we present a strongly polynomial algorithm for this problem with time complexity \(O(m^2\log m)\), where m is the number of edges of G. Moreover, we show that these algorithms can be generalized to solve these problems with capacitated constraint.

Supported by National Natural Science Foundation of China (Nos. 11871256, 12071194), and the Basic Research Project of Qinghai (No. 2021-ZJ-703).

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References

  1. Burton, D., Toint, P.L.: On an instance of the inverse shortest paths problem. Math. Program. 53(1–3), 45–61 (1992)

    Article  MathSciNet  Google Scholar 

  2. Cai, M.-C., Duin, C.W., Yang, X., Zhang, J.: The partial inverse minimum spanning tree problem when weight increasing is forbidden. Eur. J. Oper. Res. 188, 348–353 (2008)

    Article  Google Scholar 

  3. Camerini, P.M.: The min-max spanning tree problem and some extensions. Inf. Process. Lett. 7(1), 10–14 (1978)

    Article  MathSciNet  Google Scholar 

  4. Demange, M., Monnot, J.: An Introduction to Inverse Combinatorial Problems, 2nd edn. In: Paschos, V.T. (ed.) Paradigms of Combinatorial Optimization. Wliey, Hoboken (2014)

    Google Scholar 

  5. Heuberger, C.: Inverse combinatorial optimization: a survey on problems, methods, and results. J. Comb. Optim. 8(3), 329–361 (2004)

    Article  MathSciNet  Google Scholar 

  6. Li, S., Zhang, Z., Lai, H.-J.: Algorithms for constraint partial inverse matroid problem with weight increase forbidden. Theor. Comput. Sci. 640, 119–124 (2016)

    Article  MathSciNet  Google Scholar 

  7. Li, X., Zhang, Z., Du, D.-Z.: Partial inverse maximum spanning tree in which weight can only be decreased under \(l_p\)-norm. J. Global Optim. 70, 677–685 (2018)

    Article  MathSciNet  Google Scholar 

  8. Li, X., Shu, X., Huang, H., Bai, J.: Capacitated partial inverse maximum spanning tree under the weighted Hamming distance. J. Comb. Optim. 38, 1005–1018 (2019)

    Article  MathSciNet  Google Scholar 

  9. Li, X., Zhang, Z., Yang, R., Zhang, H., Du, D.-Z.: Approximation algorithms for capacitated partial inverse maximum spanning tree problem. J. Global Optim. 77(2), 319–340 (2020)

    Article  MathSciNet  Google Scholar 

  10. Li, X., Yang, R., Zhang, H., Zhang, Z.: Capacitated partial inverse maximum spanning tree under the weighted \(l_{\infty }\)-norm. In: Du, D.-Z., Du, D., Wu, C., Xu, D. (eds.) COCOA 2021. LNCS, vol. 13135, pp. 389–399. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-92681-6_31

    Chapter  Google Scholar 

  11. Liu, L., Yao, E.: Inverse min-max spanning tree problem under the weighted sum-type Hamming distance. Theoret. Comput. Sci. 196, 28–34 (2008)

    Article  MathSciNet  Google Scholar 

  12. Liu, L., Wang, Q.: Constrained inverse min-max spanning tree problems under the weighted Hamming distance. J. Global Optim. 43, 83–95 (2009)

    Article  MathSciNet  Google Scholar 

  13. Tayyebi, J., Sepasian, A.R.: Partial inverse min-max spanning tree problem. J. Comb. Optim. 40, 1–17 (2020)

    Article  MathSciNet  Google Scholar 

  14. Yang, X., Zhang, J.: Some inverse min-max network problems under weighted \(l_1\) and \(l_{\infty }\) norms with bound constraints on changes. J. Comb. Optim. 13(2), 123–135 (2007)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, Gansu, People’s Republic of China

    Qingzhen Dong, Xianyue Li & Yu Yang

Authors
  1. Qingzhen Dong
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  2. Xianyue Li
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  3. Yu Yang
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Corresponding author

Correspondence to Xianyue Li .

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Editors and Affiliations

  1. Guangdong University of Technology, Guangzhou, China

    Qiufen Ni

  2. University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

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Dong, Q., Li, X., Yang, Y. (2022). Partial Inverse Min-Max Spanning Tree Problem Under the Weighted Bottleneck Hamming Distance. In: Ni, Q., Wu, W. (eds) Algorithmic Aspects in Information and Management. AAIM 2022. Lecture Notes in Computer Science, vol 13513. Springer, Cham. https://doi.org/10.1007/978-3-031-16081-3_30

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  • DOI: https://doi.org/10.1007/978-3-031-16081-3_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-16080-6

  • Online ISBN: 978-3-031-16081-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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