{"paper":{"title":"Gossip vs. Markov Chains, and Randomness-Efficient Rumor Spreading","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS","math.PR"],"primary_cat":"cs.DC","authors_text":"He Sun, Zeyu Guo","submitted_at":"2013-11-12T17:09:25Z","abstract_excerpt":"We study gossip algorithms for the rumor spreading problem which asks one node to deliver a rumor to all nodes in an unknown network. We present the first protocol for any expander graph $G$ with $n$ nodes such that, the protocol informs every node in $O(\\log n)$ rounds with high probability, and uses $\\tilde{O}(\\log n)$ random bits in total. The runtime of our protocol is tight, and the randomness requirement of $\\tilde{O}(\\log n)$ random bits almost matches the lower bound of $\\Omega(\\log n)$ random bits for dense graphs. We further show that, for many graph families, polylogarithmic number "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2839","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"}