Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Computers and Operations Research
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Variable neighborhood search for the degree-constrained minimum spanning tree problem
Discrete Applied Mathematics - Special issue: Third ALIO-EURO meeting on applied combinatorial optimization
Low-Degree Spanning Trees of Small Weight
SIAM Journal on Computing
Comparison of Algorithms for the Degree Constrained Minimum Spanning Tree
Journal of Heuristics
Using Lagrangian dual information to generate degree constrained spanning trees
Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
Enhanced second order algorithm applied to the capacitated minimum spanning tree problem
Computers and Operations Research
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Degree constrained minimum spanning tree problem: a learning automata approach
The Journal of Supercomputing
Mobility-Based Backbone Formation in Wireless Mobile Ad-hoc Networks
Wireless Personal Communications: An International Journal
The min-degree constrained minimum spanning tree problem: Formulations and Branch-and-cut algorithm
Discrete Applied Mathematics
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Given an undirected graph with weights associated with its edges, the min-degree constrained minimum spanning tree (md-MST) problem consists in finding a minimum spanning tree of the given graph, imposing minimum degree constraints in all nodes except the leaves. This problem was recently proposed in Almeida et al. [Min-degree constrained minimum spanning tree problem: Complexity, proprieties and formulations. Operations Research Center, University of Lisbon, Working-paper no. 6; 2006], where its theoretical complexity was characterized and showed to be NP-hard. The present paper discusses variable neighborhood search (VNS) metaheuristics addressing the md-MST. A so-called enhanced version of a second order (ESO) repetitive technique is also considered, in order to guide the search in both shaking and improvement phases of the VNS method. A Kruskal based greedy heuristic adapted to the md-MST is also presented, being used within the ESO framework. VNS randomized methodologies are also discussed. These are the first heuristics to the md-MST ever proposed in the literature. Computational experiments are conducted on instances adapted from benchmark ones used in the context of the well-known degree constraint minimum spanning tree problem. These experiments have shown that randomized VNS methods enclosing an ESO algorithm can produce very interesting results. In particular, that a simpler VNS randomized methodology might be taken into account when very high dimensional instances are under consideration.