The interval Branch-and-Prune algorithm for the discretizable molecular distance geometry problem with inexact distances

• Published in: Journal of global optimization Vol. 56; no. 3; pp. 855 - 871
• Main Authors: Lavor, Carlile, Liberti, Leo, Mucherino, Antonio
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.07.2013; Springer; Springer Nature B.V; Springer Verlag
• Subjects: Algorithms; Chemical bonds; Computer Science; Discretization; Euclidean space; Experiments; Geometry; Graphs; Hydrogen; Intervals; Linear algebra; Mathematical models; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Optimization algorithms; Proteins; Real Functions; Representations; Sensors; Studies; Three dimensional; Uncertainty; Distance geometry; Combinatorial optimization; NMR data; Interval Branch and Prune; Protein conformations
• ISSN: 0925-5001; 1573-2916
• DOI: 10.1007/s10898-011-9799-6

The Distance Geometry Problem in three dimensions consists in finding an embedding in of a given nonnegatively weighted simple undirected graph such that edge weights are equal to the corresponding Euclidean distances in the embedding. This is a continuous search problem that can be discretized under some assumptions on the minimum degree of the vertices. In this paper we discuss the case where we consider the full-atom representation of the protein backbone and some of the edge weights are subject to uncertainty within a given nonnegative interval. We show that a discretization is still possible and propose the i BP algorithm to solve the problem. The approach is validated by some computational experiments on a set of artificially generated instances.