Boolean Rank via Monomial Ideals
Commutative Algebra
2025-09-12 v1 Combinatorics
Abstract
Boolean matrix factorization (BMF) has many applications in data mining, bioinformatics, and network analysis. The goal of BMF is to decompose a given binary matrix as the Boolean product of two smaller binary matrices, revealing underlying structure in the data. When interpreting a binary matrix as the adjacency matrix of a bipartite graph, BMF is equivalent to the NP-hard biclique cover problem. By approaching this problem through the lens of commutative algebra, we utilize algebraic structures and techniques--particularly the Castelnuovo-Mumford regularity of combinatorially defined ideals--to establish new lower bounds for Boolean matrix rank.
Cite
@article{arxiv.2509.09570,
title = {Boolean Rank via Monomial Ideals},
author = {Juliann Geraci and Alexander B. Kunin and Alexandra Seceleanu},
journal= {arXiv preprint arXiv:2509.09570},
year = {2025}
}