{"paper":{"title":"Improved Distributed Expander Decomposition and Nearly Optimal Triangle Enumeration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC"],"primary_cat":"cs.DS","authors_text":"Thatchaphol Saranurak, Yi-Jun Chang","submitted_at":"2019-04-17T00:50:26Z","abstract_excerpt":"An $(\\epsilon,\\phi)$-expander decomposition of a graph $G=(V,E)$ is a clustering of the vertices $V=V_{1}\\cup\\cdots\\cup V_{x}$ such that (1) each cluster $V_{i}$ induces subgraph with conductance at least $\\phi$, and (2) the number of inter-cluster edges is at most $\\epsilon|E|$. In this paper, we give an improved distributed expander decomposition.\n  Specifically, we construct an $(\\epsilon,\\phi)$-expander decomposition with $\\phi=(\\epsilon/\\log n)^{2^{O(k)}}$ in $O(n^{2/k}\\cdot\\text{poly}(1/\\phi,\\log n))$ rounds for any $\\epsilon\\in(0,1)$ and positive integer $k$. For example, a $(0.01,1/\\te"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08037","kind":"arxiv","version":2},"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"}