{"paper":{"title":"\"Tri, Tri again\": Finding Triangles and Small Subgraphs in a Distributed Setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DC","authors_text":"Christoph Lenzen, Danny Dolev, Shir Peled","submitted_at":"2012-01-31T19:02:49Z","abstract_excerpt":"Let G = (V,E) be an n-vertex graph and M_d a d-vertex graph, for some constant d. Is M_d a subgraph of G? We consider this problem in a model where all n processes are connected to all other processes, and each message contains up to O(log n) bits. A simple deterministic algorithm that requires O(n^((d-2)/d) / log n) communication rounds is presented. For the special case that M_d is a triangle, we present a probabilistic algorithm that requires an expected O(ceil(n^(1/3) / (t^(2/3) + 1))) rounds of communication, where t is the number of triangles in the graph, and O(min{n^(1/3) log^(2/3) n /"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6652","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"}