{"paper":{"title":"Faster algorithms for k-Orthogonal Vectors in low dimension","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anita D\\\"urr, Evangelos Kipouridis, Karol W\\k{e}grzycki, Michael Lampis","submitted_at":"2025-07-15T08:45:24Z","abstract_excerpt":"In the Orthogonal Vectors problem (OV), we are given two families $A, B$ of subsets of $\\{1,\\ldots,d\\}$, each of size $n$, and the task is to decide whether there exists a pair $a \\in A$ and $b \\in B$ such that $a \\cap b = \\emptyset$. Straightforward algorithms for this problem run in $\\mathcal{O}(n^2 \\cdot d)$ or $\\mathcal{O}(2^d \\cdot n)$ time, and assuming SETH, there is no $2^{o(d)}\\cdot n^{2-\\varepsilon}$ time algorithm that solves this problem for any constant $\\varepsilon > 0$.\n  Williams (FOCS 2024) presented a $\\tilde{\\mathcal{O}}(1.35^d \\cdot n)$-time algorithm for the problem, based"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.11098","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.11098/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}