{"paper":{"title":"Finding Adam in random growing trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.SI","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"G\\'abor Lugosi, Luc Devroye, S\\'ebastien Bubeck","submitted_at":"2014-11-12T20:50:31Z","abstract_excerpt":"We investigate algorithms to find the first vertex in large trees generated by either the uniform attachment or preferential attachment model. We require the algorithm to output a set of $K$ vertices, such that, with probability at least $1-\\epsilon$, the first vertex is in this set. We show that for any $\\epsilon$, there exist such algorithms with $K$ independent of the size of the input tree. Moreover, we provide almost tight bounds for the best value of $K$ as a function of $\\epsilon$. In the uniform attachment case we show that the optimal $K$ is subpolynomial in $1/\\epsilon$, and that it "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3317","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"}