{"paper":{"title":"Effective-Resistance-Reducing Flows, Spectrally Thin Trees, and Asymmetric TSP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Nima Anari, Shayan Oveis Gharan","submitted_at":"2014-11-17T20:03:26Z","abstract_excerpt":"We show that the integrality gap of the natural LP relaxation of the Asymmetric Traveling Salesman Problem is $\\text{polyloglog}(n)$. In other words, there is a polynomial time algorithm that approximates the value of the optimum tour within a factor of $\\text{polyloglog}(n)$, where $\\text{polyloglog}(n)$ is a bounded degree polynomial of $\\log\\log(n)$. We prove this by showing that any $k$-edge-connected unweighted graph has a $\\text{polyloglog}(n)/k$-thin spanning tree.\n  Our main new ingredient is a procedure, albeit an exponentially sized convex program, that \"transforms\" graphs that do no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4613","kind":"arxiv","version":4},"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"}