An Algorithm for Finding the Smallest Set of Smallest Rings

This paper describes an algorithm which finds the smallest set of smallest rings of a ring system without the necessity of finding all rings in the ring system. The algorithm first finds the smallest rings in which unused atoms occur and then progresses to find the smallest rings in which unused edges and faces occur until the smallest set of rings required to describe the complete ring system is found. The algorithm converges quickly because the lengths of the paths that need to be scanned to discover each new ring decrease when a smaller ring is found.