🤖 AI Summary
This study addresses the need for efficient enumeration of set partitions in combinatorial optimization and related domains. The authors systematically evaluate the performance of several existing enumeration algorithms and propose approximation formulas for estimating the number of set partitions that balance accuracy and computational efficiency across both small- and large-scale instances. Through comprehensive benchmarking, the algorithm by Djokic et al. is identified as the most effective in practical applications. The primary contributions include an empirical comparison of prominent set partition enumeration methods and the derivation of scalable approximation formulas that provide practitioners with clear guidance for algorithm selection and rapid estimation of partition counts.
📝 Abstract
Set partitions are arrangements of distinct objects into groups. The problem of listing all set partitions arises in a variety of settings, in particular in combinatorial optimization tasks. After a brief review, we give practical approximate formulas for determining the number of set partitions, both for small and large set sizes. Several algorithms for enumerating all set partitions are reviewed, and benchmarking tests were conducted. The algorithm of Djokic et al. is recommended for practical use.