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The Schreier-Sims algorithm is an efficient method of computing a [[strong generating set]] (SGS) 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|computer algebra systems]] 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> [[generator|generators]]. For the [[deterministic]] version of the algorithm, possible running times are:
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