Nuclear magnetic resonance(NMR) spectroscopy is widely used to solve protein structure. There are three steps to determin protein structure by NMR. Data generated by NMR is called resonance peaks. A spin system is a group of resonance peaks that corresponding to the same amino acide, which is the basic character of the protein sequence. One of the interesting computing problem is NMR spectral peak assignment eg how to relate spin systems with amino acids.
This NMR spectral peak assignment can be viewed as a Constrained Bipartite Matching problem (CBM). We view each spin system as a vertex in set V and each amino acid as a vertex in set U. Edges between U and V represent potential assignments. The edges may be weighted which specify the preference of a particular assignment. The constraint of the CBM problem is introduced by the biological fact: Spin systems from one NMR experiment are known to belong to the consecutive amino acides.
2-string unweighted CBM
2-string unweighted CBM is MAX SNP-hard