{"paper":{"title":"Almost optimal sparsification of random geometric graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.NI","math.CO"],"primary_cat":"math.PR","authors_text":"Gabor Lugosi, Luc Devroye, Nicolas Broutin","submitted_at":"2014-03-05T21:15:27Z","abstract_excerpt":"A random geometric irrigation graph $\\Gamma_n(r_n,\\xi)$ has $n$ vertices identified by $n$ independent uniformly distributed points $X_1,\\ldots,X_n$ in the unit square $[0,1]^2$. Each point $X_i$ selects $\\xi_i$ neighbors at random, without replacement, among those points $X_j$ ($j\\neq i$) for which $\\|X_i-X_j\\| < r_n$, and the selected vertices are connected to $X_i$ by an edge. The number $\\xi_i$ of the neighbors is an integer-valued random variable, chosen independently with identical distribution for each $X_i$ such that $\\xi_i$ satisfies $1\\le \\xi_i \\le \\kappa$ for a constant $\\kappa>1$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1274","kind":"arxiv","version":2},"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"}