The problem of the optimal biobjective spanning tree

This paper studies the problem of finding the set of optimal spanning trees of a connected graph, considering two cost functions defined on the set of edges. This problem is NP-hard and the solution is described through an algorithm that builds the family of efficient trees. This algorithm needs two procedures that solve the following uniobjective problems: the construction of all the spanning trees of a connected graph and the construction of the whole set of minimum cost spanning trees. The computational results obtained are shown.