<s>
The	O
Schreier	B-Algorithm
–	I-Algorithm
Sims	I-Algorithm
algorithm	I-Algorithm
is	O
an	O
algorithm	O
in	O
computational	O
group	O
theory	O
,	O
named	O
after	O
the	O
mathematicians	O
Otto	O
Schreier	O
and	O
Charles	O
Sims	O
.	O
</s>
<s>
This	O
algorithm	O
can	O
find	O
the	O
order	O
of	O
a	O
finite	O
permutation	B-Algorithm
group	I-Algorithm
,	O
test	O
membership	O
(	O
is	O
a	O
given	O
permutation	O
contained	O
in	O
a	O
group	O
?	O
</s>
<s>
Later	O
,	O
an	O
even	O
faster	O
randomized	B-General_Concept
version	O
of	O
the	O
algorithm	O
was	O
developed	O
.	O
</s>
<s>
The	O
algorithm	O
is	O
an	O
efficient	O
method	O
of	O
computing	O
a	O
base	O
and	O
strong	B-Algorithm
generating	I-Algorithm
set	I-Algorithm
(	O
BSGS	O
)	O
of	O
a	O
permutation	B-Algorithm
group	I-Algorithm
.	O
</s>
<s>
Since	O
the	O
SGS	O
is	O
critical	O
for	O
many	O
algorithms	O
in	O
computational	O
group	O
theory	O
,	O
computer	B-General_Concept
algebra	I-General_Concept
systems	I-General_Concept
typically	O
rely	O
on	O
the	O
Schreier	B-Algorithm
–	I-Algorithm
Sims	I-Algorithm
algorithm	I-Algorithm
for	O
efficient	O
calculations	O
in	O
groups	O
.	O
</s>
<s>
The	O
use	O
of	O
Schreier	B-Algorithm
vectors	I-Algorithm
can	O
have	O
a	O
significant	O
influence	O
on	O
the	O
performance	O
of	O
implementations	O
of	O
the	O
Schreier	B-Algorithm
–	I-Algorithm
Sims	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
For	O
Monte	O
Carlo	O
variations	O
of	O
the	O
Schreier	B-Algorithm
–	I-Algorithm
Sims	I-Algorithm
algorithm	I-Algorithm
,	O
we	O
have	O
the	O
following	O
estimated	O
complexity	O
:	O
</s>
<s>
In	O
modern	O
computer	B-General_Concept
algebra	I-General_Concept
systems	I-General_Concept
,	O
such	O
as	O
GAP	B-General_Concept
and	O
Magma	B-General_Concept
,	O
an	O
optimized	O
Monte	O
Carlo	O
algorithm	O
is	O
typically	O
used	O
.	O
</s>
<s>
Following	O
is	O
C++	O
-style	O
pseudo-code	O
for	O
the	O
basic	O
idea	O
of	O
the	O
Schreier-Sims	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
In	O
place	O
of	O
the	O
orbit	O
tree	O
,	O
a	O
Schreier	B-Algorithm
vector	I-Algorithm
can	O
be	O
used	O
,	O
but	O
the	O
idea	O
is	O
essentially	O
the	O
same	O
.	O
</s>
