A New Approach for Speeding Up Enumeration Algorithms and Its Application for Matroid Bases

We propose a new approach for speeding up enumeration algorithms. The approach does not rely on data structures deeply, instead utilizes analysis of computation time. It speeds enumeration algorithms for directed spanning trees, matroid bases, and some bipartite matching problems. We show one of these improved algorithms: one for enumerating matroid bases. For a given matroid M with m elements and rank n, an existing algorithm runs in O(T ) time per base. We improved the time complexity to O(T/n), or O(T/m(m−n)).