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Exact and heuristic solutions for the Minimum Number of Branch Vertices Spanning Tree Problem

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  • Marín, Alfredo

Abstract

The Minimum Number of Branch Vertices Spanning Tree Problem is to minimize the number of vertices of degree greater than two in a spanning tree. We present a branch-and-cut algorithm based on an enforced Integer Programming formulation, which can solve many more instances than previous methods. Since the problem is NP-hard, very large instances cannot be solved exactly. For such cases, a new heuristic two-stage method that gives very good approximate solutions is developed.

Suggested Citation

  • Marín, Alfredo, 2015. "Exact and heuristic solutions for the Minimum Number of Branch Vertices Spanning Tree Problem," European Journal of Operational Research, Elsevier, vol. 245(3), pages 680-689.
    • Handle: RePEc:eee:ejores:v:245:y:2015:i:3:p:680-689
    DOI: 10.1016/j.ejor.2015.04.011
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    References listed on IDEAS

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    1. Cerrone, C. & Cerulli, R. & Raiconi, A., 2014. "Relations, models and a memetic approach for three degree-dependent spanning tree problems," European Journal of Operational Research, Elsevier, vol. 232(3), pages 442-453.
    2. R. Cerulli & M. Gentili & A. Iossa, 2009. "Bounded-degree spanning tree problems: models and new algorithms," Computational Optimization and Applications, Springer, vol. 42(3), pages 353-370, April.
    3. Francesco Carrabs & Raffaele Cerulli & Manlio Gaudioso & Monica Gentili, 2013. "Lower and upper bounds for the spanning tree with minimum branch vertices," Computational Optimization and Applications, Springer, vol. 56(2), pages 405-438, October.
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