{"paper":{"title":"An Equivalence Class for Orthogonal Vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Lijie Chen, Ryan Williams","submitted_at":"2018-11-29T08:48:06Z","abstract_excerpt":"The Orthogonal Vectors problem ($\\textsf{OV}$) asks: given $n$ vectors in $\\{0,1\\}^{O(\\log n)}$, are two of them orthogonal? $\\textsf{OV}$ is easily solved in $O(n^2 \\log n)$ time, and it is a central problem in fine-grained complexity: dozens of conditional lower bounds are based on the popular hypothesis that $\\textsf{OV}$ cannot be solved in (say) $n^{1.99}$ time. However, unlike the APSP problem, few other problems are known to be non-trivially equivalent to $\\textsf{OV}$.\n  We show $\\textsf{OV}$ is truly-subquadratic equivalent to several fundamental problems, all of which (a priori) look"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12017","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"}