{"paper":{"title":"Solving Totally Unimodular LPs with the Shadow Vertex Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anna Gro{\\ss}wendt, Heiko R\\\"oglin, Tobias Brunsch","submitted_at":"2014-12-17T13:33:23Z","abstract_excerpt":"We show that the shadow vertex simplex algorithm can be used to solve linear programs in strongly polynomial time with respect to the number $n$ of variables, the number $m$ of constraints, and $1/\\delta$, where $\\delta$ is a parameter that measures the flatness of the vertices of the polyhedron. This extends our recent result that the shadow vertex algorithm finds paths of polynomial length (w.r.t. $n$, $m$, and $1/\\delta$) between two given vertices of a polyhedron.\n  Our result also complements a recent result due to Eisenbrand and Vempala who have shown that a certain version of the random"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5381","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"}