Euclidean distance geometry and applications

Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances. We survey some of the theory of Euclidean distance geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics.Comment: 64 pages, 21 figure

Proceedings of the XIII Global Optimization Workshop: GOW'16

[Excerpt] Preface: Past Global Optimization Workshop shave been held in Sopron (1985 and 1990), Szeged (WGO, 1995), Florence (GO’99, 1999), Hanmer Springs (Let’s GO, 2001), Santorini (Frontiers in GO, 2003), San José (Go’05, 2005), Mykonos (AGO’07, 2007), Skukuza (SAGO’08, 2008), Toulouse (TOGO’10, 2010), Natal (NAGO’12, 2012) and Málaga (MAGO’14, 2014) with the aim of stimulating discussion between senior and junior researchers on the topic of Global Optimization. In 2016, the XIII Global Optimization Workshop (GOW’16) takes place in Braga and is organized by three researchers from the University of Minho. Two of them belong to the Systems Engineering and Operational Research Group from the Algoritmi Research Centre and the other to the Statistics, Applied Probability and Operational Research Group from the Centre of Mathematics. The event received more than 50 submissions from 15 countries from Europe, South America and North America. We want to express our gratitude to the invited speaker Panos Pardalos for accepting the invitation and sharing his expertise, helping us to meet the workshop objectives. GOW’16 would not have been possible without the valuable contribution from the authors and the International Scientific Committee members. We thank you all. This proceedings book intends to present an overview of the topics that will be addressed in the workshop with the goal of contributing to interesting and fruitful discussions between the authors and participants. After the event, high quality papers can be submitted to a special issue of the Journal of Global Optimization dedicated to the workshop. [...

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

A symmetry-driven BP algorithm for the Discretizable Molecular Distance Geometry Problem

International audienceBranch & Prune (BP) is a deterministic algorithm for the solution of the Discretizable Molecular Distance Geometry Problem (DMDGP). This problem has important applications in the field of structural biology, in particular for the determination of the three-dimensional conformation of a molecule by using information obtained by NMR techniques. In recent works, we proved that the search domain of the DMDGP, which is represented by a binary tree, contains various symmetries which are related to the number of solutions to the problem. In the present work, we propose a variant of the BP algorithm which is able to exploit the information regarding the symmetries to speed up the search. Computational experiments show that the symmetry-driven BP (symBP) outperforms the original BP algorithm in particular when instances having several solutions are considered

Exploiting Symmetry Properties of the Discretizable Molecular Distance Geometry Problem

International audienceThe Discretizable Molecular Distance Geometry Problem (DMDGP) consists in a subset of instances of the distance geometry problem for which some assumptions allowing for discretization are satisfied. The search domain for the DMDGP is a binary tree that can be efficiently explored by employing a Branch & Prune (BP) algorithm. We showed in recent works that this binary tree may contain several symmetries, which are directly related to the total number of solutions of DMDGP instances. In this paper, we study the possibility of exploiting these symmetries for speeding up the solution of DMDGPs, and propose an extension of the BP algorithm that we named symmetry-driven BP (symBP). Computational experiments on artificial and protein instances are presented

Energy-based Pruning Devices For The Bp Algorithm Applied To Distance Geometry

The Molecular Distance Geometry Problem (MDGP) is the one of finding an embedding of a molecular graph in the three dimensional space, where graph vertices represent atoms and edges represent known distances between some pairs of atoms. The MDGP is a constraint satisfaction problem and it is generally cast as a continuous global optimization problem. Moreover, under some assumptions, this optimization problem can be discretized and so that it becomes combinatorial, and it can be solved by a Branch & Prune (BP) algorithm. The solution set found by BP, however, can be very large for some instances, while only the most energetically stable conformations are of interest. In this work, we propose and integrate the BP algorithm with two new energy-based pruning devices. Computational experiments show that the newly added pruning devices are able to improve the performance of the BP algorithm, as well as the quality (in terms of energy) of the conformations in the solution set. © 2013 Polish Information Processing Society.341346Ministry of Science and Higher Eduction,IntelCrippen, G., Havel, T., (1988) Distance Geometry and Molecular Conformation, , New York: John Wiley &SonsMucherino, A., Lavor, C., Liberti, N.M.L., (2013) Distance Geometry: Theory, Methods and Applications, p. 410. , SpringerSaxe, J.B., Embeddability of weighted graphs in k-space is strongly nphard (1979) Proceedings of 17th Allerton Conference in Communications, Control and Computing, Monticello, IL, pp. 480-489Liberti, L., Lavor, C., MacUlan, N., Mucherino, A., Euclidean distance geometry and applications (2013) To Appear in SIAM ReviewLavor, C., Liberti, L., MacUlan, N., Mucherino, A., The discretizable molecular distance geometry problem (2012) Computational Optimization and Applications, 52, pp. 115-146Liberti, L., Lavor, C., Mucherino, A., MacUlan, N., Molecular distance geometry methods: From continuous to discrete (2010) International Transactions in Operational Research, 18, pp. 33-51Lavor, C., Liberti, L., MacUlan, N., Mucherino, A., Recent advances on the discretizable molecular distance geometry problem (2012) European Journal of Operational Research, 219, pp. 698-706Liberti, L., Lavor, C., MacUlan, N., A branch-and-prune algorithm for the molecular distance geometry problem (2008) International Transactions in Operational Research, 15, pp. 1-17Lavor, C., Liberti, L., Mucherino, A., MacUlan, N., On a discretizable subclass of instances of the molecular distance geometry problem (2009) ACM Conference Proceedings, 24th Annual ACM Symposium on Applied Computing, pp. 804-805. , Hawaii, USAMucherino, A., Lavor, C., Malliavin, T., Liberti, L., Nilges, M., MacUlan, N., Influence of pruning devices on the solution of molecular distance geometry problems (2011) Proceedings of the 10th International Symposium on Experimental Algorithms (SEA11), Ser. Lecture Notes in Computer Science, 6630, pp. 206-217. , P. M. Pardalos and S. Rebennack, Eds., Crete, GreeceBondi, A., Van der waals volumes and radii (1964) Journal of Physical Chemistry, 68 (3), pp. 441-451Jones, J.E.L., Cohesion (1931) Proceedings of the Physical Society, 43, pp. 461-482Mucherino, A., Lavor, C., Liberti, L., A symmetry-driven bp algorithm for the discretizable molecular distance geometry problem (2011) IEEE Conference Proceedings, Computational Structural Bioinformatics Workshop (CSBW11), International Conference on Bioinformatics &Biomedicine (BIBM11, pp. 390-395. , Atlanta, GA, USAMucherino, A., Lavor, C., Liberti, L., Exploiting symmetry properties of the discretizable molecular distance geometry problem (2012) Journal of Bioinformatics and Computational Biology, 10, pp. 1-15. , 1242009Liberti, L., Masson, B., Lee, J., Lavor, C., Mucherino, A., On the number of solutions of the discretizable molecular distance geometry problem (2011) Proceedings of the 5th Annual International Conference on Combinatorial Optimization and Applications (COCOA11), Ser. Lecture Notes in Computer Science, 6831, pp. 322-342Linge, J.P., Nilges, M., Influence of non-bonded parameters on the quality of nmr structures: A new force field for nmr structure calculation (1999) Journal of Biomolecular NMR, 13 (1), pp. 51-59Hamaker, H.C., The london-van der waals attraction between spherical particles (1937) Physica, 4 (10), pp. 1058-1072Malliavin, T.E., Mucherino, A., Nilges, M., Distance geometry in structural biology: New perspectives (2013) Distance Geometry: Theory, Methods and Applications, pp. 329-350. , L. L. N. M. A. Mucherino, C. Lavor, Ed. SpringerBerman, H., Westbrook, J., Feng, Z., Gilliland, G., Bhat, T., Weissig, H., Shindyalov, I., Bourne, P., The protein data bank (2000) Nucleic Acids Research, 28, pp. 235-242Lavor, C., Liberti, L., Mucherino, A., The interval branch-and-prune algorithm for the discretizable molecular distance geometry problem with inexact distances (2013) Journal of Global Optimization, 56 (3), pp. 855-87

EXPLOITING SYMMETRY PROPERTIES OF THE DISCRETIZABLE MOLECULAR DISTANCE GEOMETRY PROBLEM

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)The Discretizable Molecular Distance Geometry Problem (DMDGP) involves a subset of instances of the distance geometry problem for which some assumptions allowing for discretization are satisfied. The search domain for the DMDGP is a binary tree that can be effciently explored by employing a Branch & Prune (BP) algorithm. We showed in recent works that this binary tree may contain several symmetries, which are directly related to the total number of solutions of DMDGP instances. In this paper, we study the possibility of exploiting these symmetries for speeding up the solution of DMDGPs, and propose an extension of the BP algorithm that we named symmetry-driven BP (symBP). Computational experiments on artificial and protein instances are presented.103SIANRFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)French research agency CNRSEcole PolytechniqueFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq