An efficient implementation of a quasi-polynomial algorithm for generating hypergraph transversals and its application in joint generation Original Research Article

Given a finite set image, and a hypergraph image, the hypergraph transversal problem calls for enumerating all minimal hitting sets (transversals) for image. This problem plays an important role in practical applications as many other problems were shown to be polynomially equivalent to it. Fredman and Khachiyan [On the complexity of dualization of monotone disjunctive normal forms, J. Algorithms 21 (1996) 618–628] gave an incremental quasi-polynomial-time algorithm for solving the hypergraph transversal problem. In this paper, we present an efficient implementation of this algorithm. While we show that our implementation achieves the same theoretical worst-case bound, practical experience with this implementation shows that it can be substantially faster. We also show that a slight modification of the original algorithm can be used to obtain a stronger bound on the running time.