{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-integer-programming-discrepancy-and","title":"On Integer Programming, Discrepancy, and Convolution","arxiv_id":"1803.04744","date":"2018-03-13","proceeding":null,"authors":["Klaus Jansen","Lars Rohwedder"],"abstract":"Integer programs with m constraints are solvable in pseudo-polynomial time in $\\Delta$, the largest coefficient in a constraint, when m is a fixed constant. We give a new algorithm with a running time of $O(\\sqrt{m}\\Delta)^{2m} + O(nm)$, which improves on the state-of-the-art. Moreover, we show that improving on our algorithm for any $m$ is equivalent to improving over the quadratic time algorithm for $(\\min,~+)$-convolution. This is a strong evidence that our algorithm's running time is the best possible. We also present a specialized algorithm with running time $O(\\sqrt{m} \\Delta)^{(1 + o(1))m} + O(nm)$ for testing feasibility of an integer program and also give a tight lower bound, which is based on the SETH in this case.","url_abs":"https://arxiv.org/abs/1803.04744v4","url_pdf":"https://arxiv.org/pdf/1803.04744v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"on-integer-programming-discrepancy-and","repo_url":"https://github.com/tim-we/intopt","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}