Alexandre Salles da Cunha

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Given an undirected graph G with penalties associated with its vertices and costs associated with its edges, a Prize Collecting Steiner (PCS) tree is either an isolated vertex of G or else any tree of G, be it spanning or not. The weight of a PCS tree equals the sum of the costs for its edges plus the sum of the penalties for the vertices of G not spanned(More)
1 ABSTRACT The numerical solution of problems in science and engineering via the finite element method requires, as a first step, the discretization of a domain into a set of simply shaped elements. Determining the size of these elements along the domain, including the boundary, to form well-shaped elements is a difficult task. We present in this paper a(More)
Given a connected and undirected graph, the quadratic minimum spanning tree problem consists of<lb>finding one spanning tree that minimizes a quadratic cost function. We first propose an integer program-<lb>ming formulation based on the reformulation-linearization technique and show that such a formulation<lb>is stronger than previous ones in the(More)
A new exact solution algorithm is proposed for the Degree-Constrained Minimum Spanning Tree Problem. The algorithm involves two combined phases. The first one contains a Lagrangian Relaxand-Cut procedure while the second implements a Branch-and-Cut algorithm. Both phases rely on a standard formulation for the problem, reinforced with Blossom Inequalities.(More)