{"paper":{"title":"Understanding the Correlation Gap for Matchings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Euiwoong Lee, Guru Guruganesh","submitted_at":"2017-10-17T15:14:44Z","abstract_excerpt":"Given a set of vertices $V$ with $|V| = n$, a weight vector $w \\in (\\mathbb{R}^+ \\cup \\{ 0 \\})^{\\binom{V}{2}}$, and a probability vector $x \\in [0, 1]^{\\binom{V}{2}}$ in the matching polytope, we study the quantity $\\frac{E_{G}[ \\nu_w(G)]}{\\sum_{(u, v) \\in \\binom{V}{2}} w_{u, v} x_{u, v}}$ where $G$ is a random graph where each edge $e$ with weight $w_e$ appears with probability $x_e$ independently, and let $\\nu_w(G)$ denotes the weight of the maximum matching of $G$. This quantity is closely related to correlation gap and contention resolution schemes, which are important tools in the design "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06339","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"}