Totally $\Delta$-modular IPs with two non-zeros in most rows
Data Structures and Algorithms
2025-03-19 v2 Discrete Mathematics
Combinatorics
Optimization and Control
Abstract
Integer programs (IPs) on constraint matrices with bounded subdeterminants are conjectured to be solvable in polynomial time. We give a strongly polynomial time algorithm to solve IPs where the constraint matrix has bounded subdeterminants and at most two non-zeros per row after removing a constant number of rows and columns. This result extends the work by Fiorini, Joret, Weltge \& Yuditsky (J. ACM 72(1), 1-50 (2025)) by allowing for additional, unifying constraints and variables.
Cite
@article{arxiv.2411.15282,
title = {Totally $\Delta$-modular IPs with two non-zeros in most rows},
author = {Stefan Kober},
journal= {arXiv preprint arXiv:2411.15282},
year = {2025}
}
Comments
IPCO 2025 extended version