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

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.