{"paper":{"title":"Quadratic diameter bounds for dual network flow polyhedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.OC","authors_text":"Elisabeth Finhold, Raymond Hemmecke, Steffen Borgwardt","submitted_at":"2014-08-19T00:42:27Z","abstract_excerpt":"Both the combinatorial and the circuit diameters of polyhedra are of interest to the theory of linear programming for their intimate connection to a best-case performance of linear programming algorithms.\n  We study the diameters of dual network flow polyhedra associated to $b$-flows on directed graphs $G=(V,E)$ and prove quadratic upper bounds for both of them: the minimum of $(|V|-1)\\cdot |E|$ and $\\frac{1}{6}|V|^3$ for the combinatorial diameter, and $\\frac{|V|\\cdot (|V|-1)}{2}$ for the circuit diameter. The latter strengthens the cubic bound implied by a result in [De Loera, Hemmecke, Lee;"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4184","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"}