Approximating minimum keys and optimal substructure screens

Abstract

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., finding 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.