{"paper":{"title":"The Input/Output Complexity of Sparse Matrix Multiplication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Morten St\\\"ockel, Rasmus Pagh","submitted_at":"2014-03-14T12:18:26Z","abstract_excerpt":"We consider the problem of multiplying sparse matrices (over a semiring) where the number of non-zero entries is larger than main memory. In the classical paper of Hong and Kung (STOC '81) it was shown that to compute a product of dense $U \\times U$ matrices, $\\Theta \\left(U^3 / (B \\sqrt{M}) \\right)$ I/Os are necessary and sufficient in the I/O model with internal memory size $M$ and memory block size $B$.\n  In this paper we generalize the upper and lower bounds of Hong and Kung to the sparse case. Our bounds depend of the number $N = \\mathtt{nnz}(A)+\\mathtt{nnz}(C)$ of nonzero entries in $A$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3551","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"}