{"paper":{"title":"A Subquadratic Algorithm for 3XOR","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Martin Dietzfelbinger, Philipp Schlag, Stefan Walzer","submitted_at":"2018-04-30T09:04:20Z","abstract_excerpt":"Given a set $X$ of $n$ binary words of equal length $w$, the 3XOR problem asks for three elements $a, b, c \\in X$ such that $a \\oplus b=c$, where $ \\oplus$ denotes the bitwise XOR operation. The problem can be easily solved on a word RAM with word length $w$ in time $O(n^2 \\log{n})$. Using Han's fast integer sorting algorithm (2002/2004) this can be reduced to $O(n^2 \\log{\\log{n}})$. With randomization or a sophisticated deterministic dictionary construction, creating a hash table for $X$ with constant lookup time leads to an algorithm with (expected) running time $O(n^2)$. At present, seeming"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.11086","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"}