Molecular distance geometry methods: from continuous to discrete

@article{Liberti2011MolecularDG,
  title={Molecular distance geometry methods: from continuous to discrete},
  author={Leo Liberti and Carlile Lavor and Antonio Mucherino and Nelson Maculan},
  journal={Int. Trans. Oper. Res.},
  year={2011},
  volume={18},
  pages={33-51}
}
Distance geometry problems (DGP) arise from the need to position entities in the Euclidean K-space given some of their respective distances. Entities may be atoms (molecular distance geometry), wireless sensors (sensor network localization), or abstract vertices of a graph (graph drawing). In the context of molecular distance geometry, the distances are usually known because of chemical properties and nuclear magnetic resonance experiments; sensor networks can estimate their relative distance… 

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References

SHOWING 1-10 OF 61 REFERENCES
A Geometric Build-Up Algorithm for Solving the Molecular Distance Geometry Problem with Sparse Distance Data
TLDR
A geometric build-up algorithm for solving protein structure by using only a sparse set of inter-atomic distances, which reduces the need of estimating the “missing” distances and promises a more efficient approach to NMR structure modeling.
On a discretizable subclass of instances of the molecular distance geometry problem
TLDR
A Branch and Prune algorithm is presented which can be used for obtaining a set of positions of the atoms of protein conformations when only some of the distances between the atoms are known.
A linear-time algorithm for solving the molecular distance geometry problem with exact inter-atomic distances
TLDR
A linear-time algorithm for solving the molecular distance geometry problem with exact distances between all pairs of atoms that exploits the problem structure and hence is able to identify infeasible data more easily as well.
The Branch and Prune Algorithm for the Molecular Distance Geometry Problem with Inexact Distances
TLDR
A modified version of the Branch and Prune algorithm, previously proposed for solving instances of distance geometry instances, is presented, where it is supposed that exact distances are not known, but rather intervals where the actual distances are contained.
The Molecule Problem: Exploiting Structure in Global Optimization
TLDR
This paper presents a novel divide-and-conquer algorithm in which a large global optimization problem is replaced by a sequence of smaller ones, and describes an implementation and some results of its performance on a sample molecule.
Comparisons between an exact and a metaheuristic algorithm for the molecular distance geometry problem
TLDR
The performances of two different algorithms for solving the Discretizable Molecular Distance Geometry Problem are investigated, one of which is the Branch and Prune algorithm and the other is the Monkey Search algorithm, a meta-heuristic algorithm inspired by the behavior of a monkey climbing trees in search for food supplies.
On generating Instances for the Molecular Distance Geometry Problem
TLDR
The aim of this study is to generate new instances for the molecular distance geometry problem that can be used in order to test algorithms designed to solve it.
Computational Experience with the Molecular Distance Geometry Problem
TLDR
This work applies three global optimization algorithms (spatial Branch-and-Bound, Variable Neighbourhood Search, Multi Level Single Linkage) to two sets of instances, one taken from the literature and the other new.
A Distributed SDP Approach for Large-Scale Noisy Anchor-Free Graph Realization with Applications to Molecular Conformation
TLDR
This work proposes a distributed algorithm that is able to reconstruct reliably and efficiently the configurations of large protein molecules from a limited number of pairwise distances corrupted by noise, without incorporating domain knowledge such as the minimum separation distance constraints derived from van der Waals interactions.
...
...