Maximum feasible subsystems of distance geometry constraints

We study the problem of satisfying maximum number distance geometry constraints with minimum experimental error. This models determination shape proteins from atomic data which are obtained nuclear magnetic resonance experiments and exhibit systematic errors. Experimental errors represented by interval on Euclidean distances. Systematic occur a misassignment distances to wrong pairs: we represent such maximizing satisfiable constraints. present many mathematical programming formulations, as well “matheuristic” algorithm based reformulations, relaxations, restrictions refinement. show that this works protein graphs hundreds atoms thousands