{"paper":{"title":"Separating subadditive Euclidean functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.PR","authors_text":"Alan Frieze, Wesley Pegden","submitted_at":"2015-01-08T20:15:00Z","abstract_excerpt":"If we are given $n$ random points in the hypercube $[0,1]^d$, then the minimum length of a Traveling Salesperson Tour through the points, the minimum length of a spanning tree, and the minimum length of a matching, etc., are known to be asymptotically $\\beta n^{\\frac{d-1}{d}}$ a.s., where $\\beta$ is an absolute constant in each case. We prove separation results for these constants. In particular, concerning the constants $\\beta_{\\mathrm{TSP}}^d$, $\\beta_{\\mathrm{MST}}^d$, $\\beta_{\\mathrm{MM}}^d$, and $\\beta_{\\mathrm{TF}}^d$ from the asymptotic formulas for the minimum length TSP, spanning tree"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01944","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"}