{"paper":{"title":"Distributed Symmetry Breaking in Sampling (Optimal Distributed Randomly Coloring with Fewer Colors)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Thomas P. Hayes, Weiming Feng, Yitong Yin","submitted_at":"2018-02-20T03:52:39Z","abstract_excerpt":"We examine the problem of almost-uniform sampling proper $q$-colorings of a graph whose maximum degree is $\\Delta$. A famous result, discovered independently by Jerrum(1995) and Salas and Sokal(1997), is that, assuming $q > (2+\\delta) \\Delta$, the Glauber dynamics (a.k.a. single-site dynamics) for this problem has mixing time $O(n \\log n)$, where $n$ is the number of vertices, and thus provides a nearly linear time sampling algorithm for this problem. A natural question is the extent to which this algorithm can be parallelized. Previous work Feng, Sun and Yin [PODC'17] has shown that a $O(\\Del"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06953","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"}