{"paper":{"title":"Optimizing Low Dimensional Functions over the Integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Arthur L\\'eonard, Daniel Dadush, Jos\\'e Verschae, Lars Rohwedder","submitted_at":"2023-03-04T18:10:45Z","abstract_excerpt":"We consider box-constrained integer programs with objective $g(Wx) + c^T x$, where $g$ is a \"complicated\" function with an $m$ dimensional domain. Here we assume we have $n \\gg m$ variables and that $W \\in \\mathbb Z^{m \\times n}$ is an integer matrix with coefficients of absolute value at most $\\Delta$. We design an algorithm for this problem using only the mild assumption that the objective can be optimized efficiently when all but $m$ variables are fixed, yielding a running time of $n^m(m \\Delta)^{O(m^2)}$. Moreover, we can avoid the term $n^m$ in several special cases, in particular when $c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.02474","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/2303.02474/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"}