# Improving the efficiency of branch-and-bound complete-search NMR assignment using the symmetry of molecules and spectra

## Abstract

Nuclear magnetic resonance (NMR) assignment of small molecules is presented as a typical example of a combinatorial optimization problem in chemical physics. Three strategies that help improve the efficiency of solution search by the branch and bound method are presented: 1. reduction of the size of the solution space by resort to a condensed structure formula, wherein symmetric nuclei are grouped together; 2. partitioning of the solution space based on symmetry, that becomes the basis for an efficient branching procedure; and 3. a criterion of selection of input restrictions that leads to increased gaps between branches and thus faster pruning of non-viable solutions. Although the examples chosen to illustrate this work focus on small-molecule NMR assignment, the results are generic and might help solving other combinatorial optimization problems.

- Authors:

- Ecole Polytechnique Féderale de Lausanne (EPFL), CH1-1015 Lausanne (Switzerland)
- Chemistry Department, Universidad del Valle, AA 25360 Cali, Valle (Colombia)
- (Colombia)
- MindLab Research Group, Universidad Nacional de Colombia, Bogotá D.C. (Colombia)
- DARMN Research Group, Universidad del Valle, Cali, Valle (Colombia)

- Publication Date:

- OSTI Identifier:
- 22416135

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 7; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ALLOCATIONS; BRANCHING RATIO; CHEMICAL PHYSICS; EFFICIENCY; MATHEMATICAL SOLUTIONS; MOLECULES; NMR SPECTRA; NUCLEAR MAGNETIC RESONANCE; OPTIMIZATION; SYMMETRY

### Citation Formats

```
Bernal, Andrés, Patiny, Luc, Castillo, Andrés M., MindLab Research Group, Universidad Nacional de Colombia, Bogotá D.C., González, Fabio, and Wist, Julien, E-mail: julien.wist@correounivalle.edu.co.
```*Improving the efficiency of branch-and-bound complete-search NMR assignment using the symmetry of molecules and spectra*. United States: N. p., 2015.
Web. doi:10.1063/1.4907898.

```
Bernal, Andrés, Patiny, Luc, Castillo, Andrés M., MindLab Research Group, Universidad Nacional de Colombia, Bogotá D.C., González, Fabio, & Wist, Julien, E-mail: julien.wist@correounivalle.edu.co.
```*Improving the efficiency of branch-and-bound complete-search NMR assignment using the symmetry of molecules and spectra*. United States. doi:10.1063/1.4907898.

```
Bernal, Andrés, Patiny, Luc, Castillo, Andrés M., MindLab Research Group, Universidad Nacional de Colombia, Bogotá D.C., González, Fabio, and Wist, Julien, E-mail: julien.wist@correounivalle.edu.co. Sat .
"Improving the efficiency of branch-and-bound complete-search NMR assignment using the symmetry of molecules and spectra". United States.
doi:10.1063/1.4907898.
```

```
@article{osti_22416135,
```

title = {Improving the efficiency of branch-and-bound complete-search NMR assignment using the symmetry of molecules and spectra},

author = {Bernal, Andrés and Patiny, Luc and Castillo, Andrés M. and MindLab Research Group, Universidad Nacional de Colombia, Bogotá D.C. and González, Fabio and Wist, Julien, E-mail: julien.wist@correounivalle.edu.co},

abstractNote = {Nuclear magnetic resonance (NMR) assignment of small molecules is presented as a typical example of a combinatorial optimization problem in chemical physics. Three strategies that help improve the efficiency of solution search by the branch and bound method are presented: 1. reduction of the size of the solution space by resort to a condensed structure formula, wherein symmetric nuclei are grouped together; 2. partitioning of the solution space based on symmetry, that becomes the basis for an efficient branching procedure; and 3. a criterion of selection of input restrictions that leads to increased gaps between branches and thus faster pruning of non-viable solutions. Although the examples chosen to illustrate this work focus on small-molecule NMR assignment, the results are generic and might help solving other combinatorial optimization problems.},

doi = {10.1063/1.4907898},

journal = {Journal of Chemical Physics},

number = 7,

volume = 142,

place = {United States},

year = {Sat Feb 21 00:00:00 EST 2015},

month = {Sat Feb 21 00:00:00 EST 2015}

}