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
the data of the graphes of