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Journal of Global Optimization

, Volume 56, Issue 3, pp 855–871 | Cite as

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

  • Carlile Lavor
  • Leo Liberti
  • Antonio Mucherino
Article

Abstract

The Distance Geometry Problem in three dimensions consists in finding an embedding in \({\mathbb{R}^3}\) 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 iBP algorithm to solve the problem. The approach is validated by some computational experiments on a set of artificially generated instances.

Keywords

Distance geometry Protein conformations NMR data Combinatorial optimization Interval Branch and Prune 

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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.Department of Applied Mathematics (IMECC-UNICAMP)State University of CampinasCampinasBrazil
  2. 2.LIX, École PolytechniquePalaiseauFrance
  3. 3.IRISA, University of Rennes 1RennesFrance

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