Gathering rights

As we saw in section , we can write with and .

We saw in section that we can reduce the size of the starting set, and thus the size of the function, using a subset of and the file system structure. We can do the same here.

For each file , we will adapt the set of rights.
let be a subset of so that `"/"`.
We have, as defined in section ,

The binary relation defined by

If , we write the equivalence class of . is the quotient set, i.e. the set of all the equivalence classes.

Let's define the function

With a given , if we correctly choose , we can factorize and . Let's call the best set that can be found for . Let's call . And let's call so that . Here is our factorization.

Thus we have replaced the data of the graph of
by
the data of the graphes of
and

which is smaller in practical cases.