{"paper":{"title":"The Huge Multiway Table Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","cs.DS","math.CO"],"primary_cat":"math.OC","authors_text":"Shmuel Onn","submitted_at":"2014-05-06T08:34:44Z","abstract_excerpt":"Deciding the existence of an $l\\times m\\times n$ integer threeway table with given line-sums is NP-complete already for fixed $l=3$, but is in P with both $l,m$ fixed. Here we consider {\\em huge} tables, where the variable dimension $n$ is encoded in {\\em binary}. Combining recent results on integer cones and Graver bases, we show that if the number of {\\em layer types} is fixed, then the problem is in P, whereas if it is variable, then the problem is in NP intersect coNP. Our treatment goes through the more general class of $n$-fold integer programming problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1189","kind":"arxiv","version":4},"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"}