2026-07-20T07:52:38Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:26285 2026-07-13T15:02:35Z ddc:004 open_access

The Cost of Cyclic Permutations and Remainder Sums in the Euclidean Algorithm Blomer, Valentin Bux, Kai-Uwe generic algorithms average case analysis Euclidean algorithm exponential sums cyclic permutations 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. The analysis of the average case relies on the asymptotic behavior of the sum of remainders in the Euclidean algorithm. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Valentin Blomer and Kai-Uwe Bux 2026 Is Part Of LIPIcs, Volume 381, 37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.AofA.2026.14 urn:nbn:de:0030-drops-262858 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2026.14 eng https://creativecommons.org/licenses/by/4.0/legalcode