{"paper":{"title":"On Integrality Ratios for Asymmetric TSP in the Sherali-Adams Hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Joseph Cheriyan, Konstantinos Georgiou, Sahil Singla, Zhihan Gao","submitted_at":"2014-05-05T16:18:01Z","abstract_excerpt":"We study the ATSP (Asymmetric Traveling Salesman Problem), and our focus is on negative results in the framework of the Sherali-Adams (SA) Lift and Project method.\n  Our main result pertains to the standard LP (linear programming) relaxation of ATSP, due to Dantzig, Fulkerson, and Johnson. For any fixed integer $t\\geq 0$ and small $\\epsilon$, $0<\\epsilon\\ll{1}$, there exists a digraph $G$ on $\\nu=\\nu(t,\\epsilon)=O(t/\\epsilon)$ vertices such that the integrality ratio for level~$t$ of the SA system starting with the standard LP on $G$ is $\\ge 1+\\frac{1-\\epsilon}{2t+3} \\approx \\frac43, \\frac65, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0945","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"}