{"paper":{"title":"Near-Linear Time Algorithm for n-fold ILPs via Color Coding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alexandra Lassota, Klaus Jansen, Lars Rohwedder","submitted_at":"2018-11-02T15:59:32Z","abstract_excerpt":"We study an important case of ILPs $\\max\\{c^Tx \\ \\vert\\ \\mathcal Ax = b, l \\leq x \\leq u,\\, x \\in \\mathbb{Z}^{n t} \\} $ with $n\\cdot t$ variables and lower and upper bounds $\\ell, u\\in\\mathbb Z^{nt}$. In $n$-fold ILPs non-zero entries only appear in the first $r$ rows of the matrix $\\mathcal A$ and in small blocks of size $s\\times t$ along the diagonal underneath. Despite this restriction many optimization problems can be expressed in this form. It is known that $n$-fold ILPs can be solved in FPT time regarding the parameters $s, r,$ and $\\Delta$, where $\\Delta$ is the greatest absolute value "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00950","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}