An Efficient Implementation of a Joint Generation Algorithm

Let C be an n-dimensional integral box, and π be a monotone property defined over the elements of C. We consider the problems of incrementally generating jointly the families Fπ and Gπ of all minimal subsets satisfying property π and all maximal subsets not satisfying property π, when π is given by a polynomial-time satisfiability oracle. Problems of this type arise in many practical applications. It is known that the above joint generation problem can be solved in incremental quasi-polynomial time. In this paper, we present an efficient implementation of this procedure. We present experimental results to evaluate our implementation for a number of interesting monotone properties π.