{"paper":{"title":"Distributed Triangle Detection via Expander Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC"],"primary_cat":"cs.DS","authors_text":"Hengjie Zhang, Seth Pettie, Yi-Jun Chang","submitted_at":"2018-07-17T18:59:09Z","abstract_excerpt":"We present improved distributed algorithms for triangle detection and its variants in the CONGEST model. We show that Triangle Detection, Counting, and Enumeration can be solved in $\\tilde{O}(n^{1/2})$ rounds. In contrast, the previous state-of-the-art bounds for Triangle Detection and Enumeration were $\\tilde{O}(n^{2/3})$ and $\\tilde{O}(n^{3/4})$, respectively, due to Izumi and LeGall (PODC 2017).\n  The main technical novelty in this work is a distributed graph partitioning algorithm. We show that in $\\tilde{O}(n^{1-\\delta})$ rounds we can partition the edge set of the network $G=(V,E)$ into "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06624","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"}