The aim of this section is to decrease the size needed to store all the information contained by an element of . We will make groups of files in , using the structure induced by the filesytem. The fact that files stored in the same directory often share the same properties or same function make it easy to use this structure.
the function that maps to the file
its parent. For example :
Let be a subset of so that "/".
Let's call the function that map to a file the
nearest parent in :
Let be the binary relation so that
If , we write the equivalence class of . is the quotient set, i.e. the set of all the equivalence classes.
We can now reduce the quantity of informations used in or by using functions whose starting set is . We have to chose correctly the set so that we can factorize or and can write and .
This amounts to the same thing as to group files that are given the same rights and to choose so that the equivalence classes match the groups.