The generalized minimum spanning tree problem: An overview of formulations, solution procedures and latest advances

In this paper, some of the main known results relative to the generalized minimum spanning tree problem are surveyed. The principal feature of this problem is related to the fact that the vertices of the graph are partitioned into a certain number of clusters and we are interested in finding a minimum-cost tree spanning a subset of vertices with precisely one vertex considered from every cluster. The paper is structured around the following main headings: problem definition, variations and practical applications, complexity aspects, integer programming formulations, exact and heuristic solution approaches developed for solving this problem. Furthermore, we also discuss some open problems and possible research directions. (C) 2019 Elsevier B.V. All rights reserved.