{"paper":{"title":"(Near)-Optimal Algorithms for Sparse Separable Convex Integer Programs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DS","authors_text":"Asaf Levin, Christoph Hunkenschr\\\"oder, Martin Kouteck\\'y, Tung Anh Vu","submitted_at":"2025-05-28T10:39:56Z","abstract_excerpt":"We study the general integer programming (IP) problem of optimizing a separable convex function over the integer points of a polytope: $\\min \\{f(\\mathbf{x}) \\mid A\\mathbf{x} = \\mathbf{b}, \\, \\mathbf{l} \\leq \\mathbf{x} \\leq \\mathbf{u}, \\, \\mathbf{x} \\in \\mathbb{Z}^n\\}$. The number of variables $n$ is a variable part of the input, and we consider the regime where the constraint matrix $A$ has small coefficients $\\|A\\|_\\infty$ and small primal or dual treedepth $\\mathrm{td}_P(A)$ or $\\mathrm{td}_D(A)$, respectively. Equivalently, we consider block-structured matrices, in particular $n$-fold, tree"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22212","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.22212/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}