Efficient iteration in admissible combinatorial classes

The exhaustive generation of combinatorial objects has a vast range of practical applications and is a common theme in the combinatorial research field. But most previous works in this area concentrate in the efficient generation of particular families of combinatorial objects. The novel approach of the work presented here is to provide efficient generic algorithms, where the input is not just the size n of the objects to be generated but a finite specification of the combinatorial class whose objects we want to list. Since the algorithms are generic, they do not exploit any particular feature of the class to be generated; nevertheless, they work in constant amortized time per generated object, that is, they generate all N objects of a given size in Θ(N) time. These algorithms are useful for both rapid prototyping and for inclusion into general purposes libraries because of their flexibility, with only a relatively modest penalty on efficiency. Furthermore, the framework presented in this paper nicely combines with the framework developed by Flajolet et al. for the enumeration and random generation of combinatorial objects, and with the framework developed by the authors for the unranking of combinatorial objects.