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Maximum feasible subsystems of distance geometry constraints


We study the problem of satisfying the maximum number of distance geometry constraints with minimum experimental error. This models the determination of the shape of proteins from atomic distance data which are obtained from nuclear magnetic resonance experiments and exhibit experimental and systematic errors. Experimental errors are represented by interval constraints on Euclidean distances. Systematic errors occur from a misassignment of distances to wrong atomic pairs: we represent such errors by maximizing the number of satisfiable distance constraints. We present many mathematical programming formulations, as well as a “matheuristic” algorithm based on reformulations, relaxations, restrictions and refinement. We show that this algorithm works on protein graphs with hundreds of atoms and thousands of distances.

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The datasets generated and analysed in this paper are available upon request from the corresponding author


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Correspondence to Leo Liberti.

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One of the authors (LL) was partly funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant agreement no. 764759.

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Bruglieri, M., Cordone, R. & Liberti, L. Maximum feasible subsystems of distance geometry constraints. J Glob Optim 83, 29–47 (2022).

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  • Protein conformation
  • Diagonally dominant programming