{"paper":{"title":"Partition bound is quadratically tight for product distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Jaikumar Radhakrishnan, Prahladh Harsha, Rahul Jain","submitted_at":"2015-12-07T10:36:22Z","abstract_excerpt":"Let $f : \\{0,1\\}^n \\times \\{0,1\\}^n \\rightarrow \\{0,1\\}$ be a 2-party function. For every product distribution $\\mu$ on $\\{0,1\\}^n \\times \\{0,1\\}^n$, we show that $$\\mathsf{CC}^\\mu_{0.49}(f) = O\\left(\\left(\\log \\mathsf{prt}_{1/8}(f) \\cdot \\log \\log \\mathsf{prt}_{1/8}(f)\\right)^2\\right),$$ where $\\mathsf{CC}^\\mu_\\varepsilon(f)$ is the distributional communication complexity of $f$ with error at most $\\varepsilon$ under the distribution $\\mu$ and $\\mathsf{prt}_{1/8}(f)$ is the {\\em partition bound} of $f$, as defined by Jain and Klauck [{\\em Proc. 25th CCC}, 2010]. We also prove a similar bound "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01968","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1512.01968/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}