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arXiv · 2411.15282

Totally $\Delta$-modular IPs with two non-zeros in most rows

Stefan Kober
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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.

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Stefan Kober. 2024-11-22. Totally $\Delta$-modular IPs with two non-zeros in most rows. https://arxiv.org/abs/2411.15282

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