{"paper":{"title":"Graph diameter, eigenvalues, and minimum-time consensus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MA"],"primary_cat":"math.OC","authors_text":"Alexander Olshevsky, Guillaume Vankeerberghen, Julien M. Hendrickx, Rapha\\\"el M. Jungers","submitted_at":"2012-11-27T15:27:44Z","abstract_excerpt":"We consider the problem of achieving average consensus in the minimum number of linear iterations on a fixed, undirected graph. We are motivated by the task of deriving lower bounds for consensus protocols and by the so-called \"definitive consensus conjecture\" which states that for an undirected connected graph G with diameter D there exist D matrices whose nonzero-pattern complies with the edges in G and whose product equals the all-ones matrix. Our first result is a counterexample to the definitive consensus conjecture, which is the first improvement of the diameter lower bound for linear co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6324","kind":"arxiv","version":3},"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"}