Integer and combinatorial optimization
Integer and combinatorial optimization
An analytical comparison of different formulations of the travelling sales man problem
Mathematical Programming: Series A and B
Computers and Operations Research
Integer Programming Formulation of Traveling Salesman Problems
Journal of the ACM (JACM)
The Irwin Handbook of Telecommunications
The Irwin Handbook of Telecommunications
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
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
A new evolutionary approach to the degree-constrained minimumspanning tree problem
IEEE Transactions on Evolutionary Computation
Improvements and extensions to the Miller-Tucker-Zemlin subtour elimination constraints
Operations Research Letters
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Mobility-Based Backbone Formation in Wireless Mobile Ad-hoc Networks
Wireless Personal Communications: An International Journal
Lower and upper bounds for the spanning tree with minimum branch vertices
Computational Optimization and Applications
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Given an undirected network with positive edge costs and a positive integer d2, the minimum-degree constrained minimum spanning tree problem is the problem of finding a spanning tree with minimum total cost such that each non-leaf node in the tree has a degree of at least d. This problem is new to the literature while the related problem with upper bound constraints on degrees is well studied. Mixed-integer programs proposed for either type of problem is composed, in general, of a tree-defining part and a degree-enforcing part. In our formulation of the minimum-degree constrained minimum spanning tree problem, the tree-defining part is based on the Miller-Tucker-Zemlin constraints while the only earlier paper available in the literature on this problem uses single and multi-commodity flow-based formulations that are well studied for the case of upper degree constraints. We propose a new set of constraints for the degree-enforcing part that lead to significantly better solution times than earlier approaches when used in conjunction with Miller-Tucker-Zemlin constraints.