Heuristic search in constrained bipartite matching with applications to protein NMR backbone resonance assignment.

The constrained bipartite matching (CBM) problem is a variant of the classical bipartite matching problem that has been well studied in the Combinatorial Optimization community. The input to CBM is an edge-weighted complete bipartite graph in which there are a same number of vertices on both sides and vertices on one side are sequentially ordered while vertices on the other side are partitioned and connected into disjoint directed paths. In a feasible matching, a path must be mapped to consecutive vertices on the other side. The optimization goal is to find a maximum or a minimum weight perfect matching. Such an optimization problem has its applications to scheduling and protein Nuclear Magnetic Resonance peak assignment. It has been shown to be NP-hard and MAX SNP-hard if the perfectness requirement is dropped. In this paper, more results on the inapproximability are presented and IDA*, a memory efficient variant of the well known A* search algorithm, is utilized to solve the problem. Accordingly, search heuristics and a set of heuristic evaluation functions are developed to assist the search, whose effectiveness is demonstrated by a simulation study using real protein NMR backbone resonance assignment instances.