An artificial intelligence approach for the generation and enumeration of perfect matchings on graphs

A new search based algorithm is developed for an effective combinatorial exploration of all the perfect matchings on a general graph. The algorithm makes use of a relations based representation of the graph and is completely independent of the nature of the graph. Though this is a typical NP-class subgraph enumeration problem, the search ranks high in selectivity without compromising accuracy using heuristic guidance. Since the present algorithm is quite compact, nonspecific and generates all perfect matchings of the graph, it excels all the earlier algorithms in its uniqueness. Further it is flexible to accommodate domain specific efficiency improvements, which is illustrated for some classes of graphs.