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An Analysis on the Degrees of Freedom of Binary Representations for Solutions to Discretizable Distance Geometry Problems

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Recent Advances in Computational Optimization (WCO 2020)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 986))

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Abstract

The degrees of freedom in special binary representations for instances of the Discretizable Distance Geometry Problem (DDGP) are studied in this note article. The focus is on DDGP instances where the underlying graphs, together with their associated vertex orders, are able to satisfy the so-called consecutivity assumption. This additional assumption, in fact, makes it possible to group together subsets of consecutive binary variables, which turn out to strongly depend on each other, so that they can actually be replaced by a smaller subset of binary variables. As a consequence, new binary representations, with reduced degrees of freedom w.r.t the trivial binary representations for DDGP instances, can be introduced and potentially be exploited in DDGP solution methods.

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Notes

  1. 1.

    The additional “M” stands for Molecular and it reminds that this class of problems seemed, when introduced, to be particularly suitable to structural biology problems.

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Acknowledgements

This work is partially supported by the international project multiBioStruct funded by the ANR French funding agency (ANR-19-CE45-0019).

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Correspondence to Antonio Mucherino .

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Mucherino, A. (2022). An Analysis on the Degrees of Freedom of Binary Representations for Solutions to Discretizable Distance Geometry Problems. In: Fidanova, S. (eds) Recent Advances in Computational Optimization. WCO 2020. Studies in Computational Intelligence, vol 986. Springer, Cham. https://doi.org/10.1007/978-3-030-82397-9_13

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