{"paper":{"title":"Hamming distance completeness and sparse matrix multiplication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Daniel Graf, Karim Labib, Przemys{\\l}aw Uzna\\'nski","submitted_at":"2017-11-10T15:41:53Z","abstract_excerpt":"We show that a broad class of $(+,\\diamond)$ vector products (for binary integer functions $\\diamond$) are equivalent under one-to-polylog reductions to the computation of the Hamming distance. Examples include: the dominance product, the threshold product and $\\ell_{2p+1}$ distances for constant $p$. Our results imply equivalence (up to polylog factors) between complexity of computation of All Pairs: Hamming Distances, $\\ell_{2p+1}$ Distances, Dominance Products and Threshold Products. As a consequence, Yuster's~(SODA'09) algorithm improves not only Matou\\v{s}ek's (IPL'91), but also the resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03887","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"}