{"ID":2823330,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2601.00979","arxiv_id":"2601.00979","title":"The cost of cyclic permutations and remainder sums in the Euclidean algorithm","abstract":"We discuss a modification to the Gries-Mills block swapping scheme for in-place rotation with average costs of 1.85 moves per element and worst case performance still at 3 moves per element. Analysis of the average case relies on the asymptotic behavior of the sum of remainders in the Euclidean algorithm.","short_abstract":"We discuss a modification to the Gries-Mills block swapping scheme for in-place rotation with average costs of 1.85 moves per element and worst case performance still at 3 moves per element. Analysis of the average case relies on the asymptotic behavior of the sum of remainders in the Euclidean algorithm.","url_abs":"https://arxiv.org/abs/2601.00979","url_pdf":"https://arxiv.org/pdf/2601.00979v1","authors":"[\"Valentin Blomer\",\"Kai-Uwe Bux\"]","published":"2026-01-02T20:12:57Z","proceeding":"cs.DS","tasks":"[\"cs.DS\"]","methods":"[]","has_code":false}