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Greedy heuristics for the diameter-constrained minimum spanning tree problem

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Abstract

The diameter-constrained minimum spanning tree problem is an NP-hard combinatorial optimization problem that seeks a minimum cost spanning tree with a limit D imposed upon the length of any path in the tree. We begin by presenting four constructive greedy heuristics and, secondly, we present some second-order heuristics, performing some improvements on feasible solutions, hopefully leading to better objective function values. We present a heuristic with an edge exchange mechanism, another that transforms a feasible spanning tree solution into a feasible diameter-constrained spanning tree solution, and finally another with a repetitive mechanism. Computational results show that repetitive heuristics can improve considerably over the results of the greedy constructive heuristics, but using a huge amount of computation time. To obtain computational results, we use instances of the problem corresponding to complete graphs with a number of nodes between 20 and 60 and with the value of D varying between 4 and 9.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade de Aveiro, Aveiro, Portugal

    C. Requejo & E. Santos

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  1. C. Requejo
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  2. E. Santos
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Correspondence to C. Requejo.

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 63, Optimal Control, 2009.

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Requejo, C., Santos, E. Greedy heuristics for the diameter-constrained minimum spanning tree problem. J Math Sci 161, 930–943 (2009). https://doi.org/10.1007/s10958-009-9611-z

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  • DOI: https://doi.org/10.1007/s10958-009-9611-z

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