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

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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.

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Authors and Affiliations

  1. Department of Applied Mathematics (IMECC-UNICAMP), State University of Campinas, Campinas, SP, 13081–970, Brazil

    Carlile Lavor

  2. LIX, École Polytechnique, 91128, Palaiseau, France

    Leo Liberti

  3. IRISA, University of Rennes 1, 35042, Rennes, France

    Antonio Mucherino

Authors
  1. Carlile Lavor
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  2. Leo Liberti
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  3. Antonio Mucherino
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Correspondence to Antonio Mucherino.

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Lavor, C., Liberti, L. & Mucherino, A. The interval Branch-and-Prune algorithm for the discretizable molecular distance geometry problem with inexact distances. J Glob Optim 56, 855–871 (2013). https://doi.org/10.1007/s10898-011-9799-6

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  • DOI: https://doi.org/10.1007/s10898-011-9799-6

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