{"paper":{"title":"Connectivity of sparse Bluetooth networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.NI","math.CO"],"primary_cat":"math.PR","authors_text":"G\\'abor Lugosi, Luc Devroye, Nicolas Broutin","submitted_at":"2014-02-15T14:27:12Z","abstract_excerpt":"Consider a random geometric graph defined on $n$ vertices uniformly distributed in the $d$-dimensional unit torus. Two vertices are connected if their distance is less than a \"visibility radius\" $r_n$. We consider {\\sl Bluetooth networks} that are locally sparsified random geometric graphs. Each vertex selects $c$ of its neighbors in the random geometric graph at random and connects only to the selected points. We show that if the visibility radius is at least of the order of $n^{-(1-\\delta)/d}$ for some $\\delta > 0$, then a constant value of $c$ is sufficient for the graph to be connected, wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3696","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"}