Abstract.
The Node Weighted Steiner Tree Problem (NW-STP) is a generalization of the Steiner Tree Problem. A lagrangean heuristic presented in EngevallS: StrLBN: 98, and based on the work in Lucena: 92, solves the problem by relaxing an exponential family of generalized subtour elimination constraints and taking into account only the violated ones as the computation proceeds. In EngevallS: StrLBN: 98 the computational results refer to complete graphs up to one hundred vertices. In this paper, we present a branch-and-bound algorithm based on this formulation. Its performance on the instances from the literature confirms the effectiveness of the approach. The experimentation on a newly generated set of benchmark problems, more similar to the real-world applications, shows that the approach is still valid, provided that suitable refinements on the bounding procedures and a preprocessing phase are introduced. The algorithm solves to optimality all of the considered instances up to one thousand vertices, with the exception of 11 hard instances, derived from the literature of a similar problem, the Prize Collecting Steiner Tree Problem.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Received: March 2005, Revised: September 2005
AMS classification:
68M10, 90C10, 90C57
This work has been partially supported by the Ministero dell'Istruzione, Universitá e Ricerca (MIUR), Italy
Rights and permissions
About this article
Cite this article
Cordone, R., Trubian, M. An exact algorithm for the node weighted Steiner tree problem. 4OR 4, 124–144 (2006). https://doi.org/10.1007/s10288-005-0081-y
Issue Date:
DOI: https://doi.org/10.1007/s10288-005-0081-y