{"paper":{"title":"New Distributed Algorithms in Almost Mixing Time via Transformations from Parallel Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC"],"primary_cat":"cs.DS","authors_text":"Jason Li, Mohsen Ghaffari","submitted_at":"2018-05-12T18:58:10Z","abstract_excerpt":"We show that many classical optimization problems --- such as $(1\\pm\\epsilon)$-approximate maximum flow, shortest path, and transshipment --- can be computed in $\\newcommand{\\tmix}{{\\tau_{\\text{mix}}}}\\tmix(G)\\cdot n^{o(1)}$ rounds of distributed message passing, where $\\tmix(G)$ is the mixing time of the network graph $G$. This extends the result of Ghaffari et al.\\ [PODC'17], whose main result is a distributed MST algorithm in $\\tmix(G)\\cdot 2^{O(\\sqrt{\\log n \\log\\log n})}$ rounds in the CONGEST model, to a much wider class of optimization problems. For many practical networks of interest, e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04764","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"}