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.
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.
References
Lavor, C., Liberti, L., Maculan, N., Mucherino, A.: The discretizable molecular distance geometry problem. Comput. Optim. Appl. 52, 115–146 (2012)
Liberti, L., Lavor, C., Maculan, N., Mucherino, A.: Euclidean distance geometry and applications. SIAM Rev. 56(1), 3–69 (2014)
Liberti, L., Masson, B., Lee, J., Lavor, C., Mucherino, A.: On the number of realizations of Certain Henneberg graphs arising in protein conformation. Discret. Appl. Math. 165, 213–232 (2014)
Mucherino, A.: A Pseudo de Bruijn graph representation for discretization orders for distance geometry. In: Ortuño, F., Rojas, I. (eds.), Proceedings of the 3rd International Work-Conference on Bioinformatics and Biomedical Engineering (IWBBIO15), Granada, Spain. Lecture Notes in Computer Science, Lecture Notes in Bioinformatics series, vol. 9043, pp. 514–523 (2015)
Mucherino, A., Lavor, C., Liberti, L.: The discretizable distance geometry problem. Optim. Lett. 6(8), 1671–1686 (2012)
Mucherino, A., Lavor, C., Liberti, L., Talbi, E.-G.: A parallel version of the branch & Prune Algorithm for the molecular distance geometry problem. In: IEEE Conference Proceedings, ACS/IEEE International Conference on Computer Systems and Applications (AICCSA10), Hammamet, Tunisia, pp. 1–6 (2010)
Mucherino, A., Liberti, L., Lavor, C.: MD-Jeep: an implementation of a branch & Prune Algorithm for distance geometry problems. In: Fukuda, K., et al. (eds.), Proceedings of the 3rd International Congress on Mathematical Software (ICMS10), Kobe, Japan. Lectures Notes in Computer Science, vol. 6327, pp. 186—197 (2010)
Saxe, J.: Embeddability of weighted graphs in \(k\)-space is strongly NP-hard. In: Proceedings of 17th Allerton Conference in Communications, Control and Computing, pp. 480–489 (1979)
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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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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DOI: https://doi.org/10.1007/978-3-030-82397-9_13
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