{"paper":{"title":"Convergence Time Analysis of Quantized Gossip Consensus on Digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"cs.SY","authors_text":"Hideaki Ishii, Kai Cai","submitted_at":"2011-05-09T13:33:07Z","abstract_excerpt":"We have recently proposed quantized gossip algorithms which solve the consensus and averaging problems on directed graphs with the least restrictive connectivity requirements. In this paper we study the convergence time of these algorithms. To this end, we investigate the shrinking time of the smallest interval that contains all states for the consensus algorithm, and the decay time of a suitable Lyapunov function for the averaging algorithm. The investigation leads us to characterizing the convergence time by the hitting time in certain special Markov chains. We simplify the structures of sta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1668","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"}