{"paper":{"title":"Parallel and sequential in-place permuting and perfect shuffling using involutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Frank Ruskey, John Ellis, Khalegh Mamakani, Qingxuan Yang","submitted_at":"2012-04-09T19:39:27Z","abstract_excerpt":"We show that any permutation of ${1,2,...,N}$ can be written as the product of two involutions. As a consequence, any permutation of the elements of an array can be performed in-place in parallel in time O(1). In the case where the permutation is the $k$-way perfect shuffle we develop two methods for efficiently computing such a pair of involutions.\n  The first method works whenever $N$ is a power of $k$; in this case the time is O(N) and space $O(\\log^2 N)$. The second method applies to the general case where $N$ is a multiple of $k$; here the time is $O(N \\log N)$ and the space is $O(\\log^2 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1958","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"}