Computers and Operations Research
Integer Programming Formulation of Traveling Salesman Problems
Journal of the ACM (JACM)
Variable neighborhood search for the degree-constrained minimum spanning tree problem
Discrete Applied Mathematics - Special issue: Third ALIO-EURO meeting on applied combinatorial optimization
Strong lower bounds for the prize collecting Steiner problem in graphs
Discrete Applied Mathematics - Brazilian symposium on graphs, algorithms and combinatorics
The Lagrangian Relaxation Method for Solving Integer Programming Problems
Management Science
The multi-weighted Steiner tree problem: A reformulation by intersection
Computers and Operations Research
VNS and second order heuristics for the min-degree constrained minimum spanning tree problem
Computers and Operations Research
Using Lagrangian dual information to generate degree constrained spanning trees
Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
Reformulation by intersection method on the MST problem with lower bound on the number of leaves
INOC'11 Proceedings of the 5th international conference on Network optimization
Improvements and extensions to the Miller-Tucker-Zemlin subtour elimination constraints
Operations Research Letters
| Hi-index | 0.04 |
Given an edge weighted undirected graph G and a positive integer d, the Min-Degree Constrained Minimum Spanning Tree Problem (MDMST) consists of finding a minimum cost spanning tree of G, such that each vertex is either a leaf or else has degree at least d in the tree. In this paper, we discuss two formulations for MDMST based on exponentially many undirected and directed subtour breaking constraints and compare the strength of their Linear Programming (LP) bounds with other bounds in the literature. Aiming to overcome the fact that the strongest of the two models, the directed one, is not symmetric with respect to the LP bounds, we also presented a symmetric compact reformulation, devised with the application of an Intersection Reformulation Technique to the directed model. The reformulation proved to be much stronger than the previous models, but evaluating its bounds is very time consuming. Thus, better computational results were obtained by a Branch-and-cut algorithm based on the original directed formulation. With the proposed method, several new optimality certificates and new best upper bounds for MDMST were provided.