Integer and combinatorial optimization
Integer and combinatorial optimization
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
A nearly best-possible approximation algorithm for node-weighted Steiner trees
Journal of Algorithms
Computers and Operations Research
Spanning Trees with Bounded Number of Branch Vertices
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
An Incremental Method for Solving Convex Finite Min-Max Problems
Mathematics of Operations Research
Bounded-degree spanning tree problems: models and new algorithms
Computational Optimization and Applications
Computers and Operations Research
On solving the Lagrangian dual of integer programs via an incremental approach
Computational Optimization and Applications
Light trees: optical multicasting for improved performance in wavelength routed networks
IEEE Communications Magazine
Improvements and extensions to the Miller-Tucker-Zemlin subtour elimination constraints
Operations Research Letters
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We study a variant of the spanning tree problem where we require that, for a given connected graph, the spanning tree to be found has the minimum number of branch vertices (that is vertices of the tree whose degree is greater than two). We provide four different formulations of the problem and compare different relaxations of them, namely Lagrangian relaxation, continuous relaxation, mixed integer-continuous relaxation. We approach the solution of the Lagrangian dual both by means of a standard subgradient method and an ad-hoc finite ascent algorithm based on updating one multiplier at the time. We provide numerical result comparison of all the considered relaxations on a wide set of benchmark instances. A useful follow-up of tackling the Lagrangian dual is the possibility of getting a feasible solution for the original problem with no extra costs. We evaluate the quality of the resulting upper bound by comparison either with the optimal solution, whenever available, or with the feasible solution provided by some existing heuristic algorithms.