Benchmarking of algorithms for set partitions
Data Structures and Algorithms
2026-02-03 v1 Discrete Mathematics
Software Engineering
Combinatorics
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.
Cite
@article{arxiv.2602.01350,
title = {Benchmarking of algorithms for set partitions},
author = {Arnav Khinvasara and Alexander Pikovski},
journal= {arXiv preprint arXiv:2602.01350},
year = {2026}
}