Schreier–Sims algorithm: Difference between revisions

Revision as of 09:47, 19 January 2011

Revision as of 20:48, 20 October 2011

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The algorithm is an efficient method of computing a [[base_(group_theory)|base]] and [[strong generating set]] (BSGS) of a [[permutation group]]. In particular, an SGS determines the order of a group and makes it easy to test membership in the group. Since the SGS is critical for many algorithms in computational group theory, [[computer algebra system]]s typically rely on the Schreier–Sims algorithm for efficient calculations in groups.

The running time of Schreier–Sims varies on the implementation. Let <math> G \leq S_n </math> be given by <math>t</math> [[generatorGenerating (mathematics)set of a group|generators]]. For the [[deterministic]] version of the algorithm, possible running times are:

* <math>O(n^2 \log^3 |G| + tn \log |G|) </math> requiring memory <math>O(n^2 \log |G| + tn)</math>