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The Molecular Distance Geometry Problem consists in finding the positions in R 3 of the atoms of a molecule, given some of the inter-atomic distances. We show that under an additional requirement on the given distances (which is realistic from the chemical point of view) this can be transformed to a combinatorial problem. We propose a Branch-and-Prune… (More)

- Carlile Lavor, Leo Liberti, Nelson Maculan, Antonio Mucherino
- Comp. Opt. and Appl.
- 2012

Given a simple weighted undirected graph G = 3 such that ||xu − xv|| = duv for each {u, v} ∈ E. We show that under a few assumptions usually satisfied in proteins, the MDGP can be formulated as a search in a discrete space. We call this MDGP subclass the Discretizable MDGP (DMDGP). We show that the DMDGP is NP-hard and we propose a solution algorithm called… (More)

- Carlile Lavor, Leo Liberti, Nelson Maculan
- Encyclopedia of Optimization
- 2009

- Laura Bahiense, Nelson Maculan, Claudia A. Sagastizábal
- Math. Program.
- 2002

- Antonio Mucherino, Leo Liberti, Carlile Lavor, Nelson Maculan
- GECCO
- 2009

We consider the Discretizable Molecular Distance Geometry Problem (DMDGP), which consists in a subclass of instances of the distance geometry problem related to molecular conformations for which a combinatorial reformulation can be supplied. We investigate the performances of two different algorithms for solving the DMDGP. The first one is the Branch and… (More)

- Carlile Lavor, Antonio Mucherino, Leo Liberti, Nelson Maculan
- 2009 International Multiconference on Computer…
- 2009

NMR experiments are able to provide some of the distances between pairs of hydrogen atoms in molecular conformations. The problem of finding the coordinates of such atoms is known as the molecular distance geometry problem. This problem can be reformulated as a combinatorial optimization problem and efficiently solved by an exact algorithm. To this purpose,… (More)

- Alexandre Salles da Cunha, Abilio Lucena, Nelson Maculan, Mauricio G. C. Resende
- Discrete Applied Mathematics
- 2009

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)

- Sergei S. Kucherenko, Pietro Belotti, Leo Liberti, Nelson Maculan
- Discrete Applied Mathematics
- 2007

Determining the maximum number of D-dimensional spheres of radius r that can be adjacent to a central sphere of radius r is known as the Kissing Number Problem (KNP). The problem has been solved for 2, 3 and very recently for 4 dimensions. We present two nonlinear (nonconvex) mathematical programming models for the solution of the KNP. We solve the problem… (More)

- Haroldo G. Santos, Eduardo Uchoa, Luiz Satoru Ochi, Nelson Maculan
- Annals OR
- 2012

This work presents an integer programming formulation for a variant of the Class-Teacher Timetabling problem, which considers the satisfaction of teacher preferences and also the proper distribution of lessons throughout the week. The formulation contains a very large number of variables and is enhanced by cuts. Therefore, a cut and column generation… (More)

- Rafael Andrade, Abilio Lucena, Nelson Maculan
- Discrete Applied Mathematics
- 2006