{"paper":{"title":"On the Shadow Simplex Method for Curved Polyhedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Daniel Dadush, Nicolai H\\\"ahnle","submitted_at":"2014-12-20T23:19:09Z","abstract_excerpt":"We study the simplex method over polyhedra satisfying certain \"discrete curvature\" lower bounds, which enforce that the boundary always meets vertices at sharp angles. Motivated by linear programs with totally unimodular constraint matrices, recent results of Bonifas et al (SOCG 2012), Brunsch and R\\\"oglin (ICALP 2013), and Eisenbrand and Vempala (2014) have improved our understanding of such polyhedra.\n  We develop a new type of dual analysis of the shadow simplex method which provides a clean and powerful tool for improving all previously mentioned results. Our methods are inspired by the re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6705","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"}