# Learning Schreier–Sims Algorithm [closed]

I am trying to learn Schreier–Sims Algorithm, and looking at Mathematics and Such - Schreier–Sims algorithm.

In the 3rd line of red/yellow box in 2nd figure in the link:

I am not sure why the 2nd and 3rd arrow are there, since it should only care about '2' this time, isn't it, why are 4, 7, 9 involved?

If can recommend any good tutorial on the Schreier–Sims Algorithm, I really appreciate.

It's following the pseudocode for the algorithm. Each of the three red/yellow boxes involves a call of the "For each $$i = 1, 2,\ldots, n$$" step, so it is looking at all points with entries not equal to $$-1$$. Note that it also looks at images of $$5$$ and $$6$$ in this step, but they yield no new points in the orbit, so there are no arrows with those points as source.
This pseudocode is not efficient because it involves repeated calls of the "For $$i = 1, 2,\ldots, n$$" step, giving complexity $$O(n^2m)$$. More efficient code keeps the points in the orbit in a queue to be processed, and has complexity $$O(nm)$$.