Implementations of the well-known Apriori algorithm for finding frequent item sets and associations rules usually rely on a doubly recursive scheme to count the subsets of a given transaction. This process can be accelerated if the recursion is restricted to those parts of the tree structure that hold the item set counters whose values are to be determined in the current pass (i.e., contain a path to the currently deepest level). In the implementation described here this is achieved by marking the active parts every time a new level is added.