We introduce the tree-decomposition-based parameter totally Δ-modular treewidth (TDM-treewidth) for matrices with two nonzero entries per row. We show how to solve integer programs whose matrices have bounded TDM-treewidth in polynomial time when variables have bounded domain. This extends previous graph-based decomposition parameters for matrices with at most two nonzero entries per row to include matrices with entries outside of {−1,0,1}. We also give an analogue of the Grid Theorem of Robertson and Seymour for matrices of bounded TDM-treewidth in the language of rooted signed graphs.
@article{arxiv.2602.01499,
title = {Totally $\Delta$-Modular Tree Decompositions of Graphic Matrices for Integer Programming},
author = {Caleb McFarland},
journal= {arXiv preprint arXiv:2602.01499},
year = {2026}
}