{"paper":{"title":"Almost quadratic gap between partition complexity and query/communication complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Andris Ambainis, Martins Kokainis","submitted_at":"2015-12-02T12:07:38Z","abstract_excerpt":"We show nearly quadratic separations between two pairs of complexity measures:\n  1. We show that there is a Boolean function $f$ with $D(f)=\\Omega((D^{sc}(f))^{2-o(1)})$ where $D(f)$ is the deterministic query complexity of $f$ and $D^{sc}$ is the subcube partition complexity of $f$;\n  2. As a consequence, we obtain that there is a communication task $f(x, y)$ such that $D^{cc}(f)=\\Omega(\\log^{2-o(1)}\\chi(f))$ where $D^{cc}(f)$ is the deterministic 2-party communication complexity of $f$ (in the standard 2-party model of communication) and $\\chi(f)$ is the partition number of $f$.\n  Both of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00661","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"}