{"paper":{"title":"Simpler derivation of bounded pitch inequalities for set covering, and minimum knapsack sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Daniel Bienstock, Mark Zuckerberg","submitted_at":"2018-06-19T19:26:06Z","abstract_excerpt":"A valid inequality \\alpha^Tx \\ge \\alpha_0 for a set covering problem is said to have pitch <= k ( a positive integer) if the k smallest positive \\alpha_j sum to at least alpha_0. This paper presents a new, simple derivation of a relaxation for set covering problems whose solutions satisfy all valid inequalities of pitch and is of polynomial size, for each fixed . We also consider the minimum knapsack problem, and show that for each fixed integer p > 0 and 0 < \\epsilon < 1 one can separate, within additive tolerance \\epsilon, from the relaxation defined by the valid inequalities with coefficien"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07435","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"}