{"paper":{"title":"The Strength of Multi-row Aggregation Cuts for Sign-pattern Integer Programs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andres Iroume, Guanyi Wang, Santanu S. Dey","submitted_at":"2017-11-19T04:06:21Z","abstract_excerpt":"In this paper, we study the strength of aggregation cuts for sign-pattern integer programs (IPs). Sign-pattern IPs are a generalization of packing IPs and are of the form $\\{x\\in \\mathbb{Z}^n_+\\ | \\ Ax\\le b\\}$ where for a given column $j$, $A_{ij}$ is either non-negative for all $i$ or non-positive for all $i$. Our first result is that the aggregation closure for such sign-pattern IPs can be 2-approximated by the original 1-row closure. This generalizes a result for packing IPs. On the other hand, unlike in the case of packing IPs, we show that the multi-row aggregation closure cannot be well "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06963","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"}