{"paper":{"title":"The I/O complexity of hybrid algorithms for square matrix multiplication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Lorenzo De Stefani","submitted_at":"2019-04-29T16:39:50Z","abstract_excerpt":"Asymptotically tight lower bounds are derived for the I/O complexity of a general class of hybrid algorithms computing the product of $n \\times n$ square matrices combining ``\\emph{Strassen-like}'' fast matrix multiplication approach with computational complexity $\\Theta{n^{\\log_2 7}}$, and ``\\emph{standard}'' matrix multiplication algorithms with computational complexity $\\Omega\\left(n^3\\right)$. We present a novel and tight $\\Omega\\left(\\left(\\frac{n}{\\max\\{\\sqrt{M},n_0\\}}\\right)^{\\log_2 7}\\left(\\max\\{1,\\frac{n_0}{M}\\}\\right)^3M\\right)$ lower bound for the I/O complexity a class of ``\\emph{u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12804","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"}