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Decomposition methods based on articulation vertices for degree-dependent spanning tree problems

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Abstract

Decomposition methods for optimal spanning trees on graphs are explored in this work. The attention is focused on optimization problems where the objective function depends only on the degrees of the nodes of the tree. In particular, we deal with the Minimum Leaves problem, the Minimum Branch Vertices problem and the Minimum Degree Sum problem. The decomposition is carried out by identifying the articulation vertices of the graph and then its blocks, solving certain subproblems on the blocks and then bringing together the optimal sub-solutions following adequate procedures. Computational results obtained using similar Integer Programming formulations for both the original and the decomposed problems show the advantage of the proposed methods on decomposable graphs.

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Acknowledgements

This work has been supported by Ministerio de Economía y Competitividad, Projects MTM2015-65915-R and MTM2015-68097-P (MINECO/FEDER), Fundación Séneca, Project 19320/PI/14 and Fundación BBVA, Project “Cost-sensitive classification. A mathematical optimization approach” (COSECLA).

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Authors and Affiliations

  1. Universidad Miguel Hernandez de Elche, Elche, Spain

    Mercedes Landete & José Luis Sainz-Pardo

  2. Universidad de Murcia, Murcia, Spain

    Alfredo Marín

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  1. Mercedes Landete
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  2. Alfredo Marín
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  3. José Luis Sainz-Pardo
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Correspondence to Mercedes Landete.

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Landete, M., Marín, A. & Sainz-Pardo, J.L. Decomposition methods based on articulation vertices for degree-dependent spanning tree problems. Comput Optim Appl 68, 749–773 (2017). https://doi.org/10.1007/s10589-017-9924-7

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