Approximating Minimum Keys and Optimal Substructure Screens

In this paper, we study the set cover problems, the minimum cardinality key problems and the optimal screen problems. We consider SET COVER-II, a variant of SET COVER, i.e., nding L sets among given n sets such that the cardinality of their union maximizes. We give both a lower bound and an upper bound to the approximation ratio of SET COVER-II and obtain a new result on SET COVER by approaching it from SET COVER-II. The minimum cardinality key problems and the optimal screen problems are more practical where the latter ones are problems of seeking a good subset from a given set of substructures and are originated from database management systems for chemical structures. We analyze the approximation ratios of those problems by reductions from/to set cover problems and give average case analyses.