Suffix Tree in Python
So, about all those globals. They make your code really hard to read, I have almost no idea what is going on (after having read it twice). The general recommendation is to only use global objects if you really have to. Otherwise pass the objects either as arguments to the function, or write a class which has the relevant variables as attributes and keep the state like this.

Another thing that makes your code a lot easier to understand (both for other people and for yourself in two months time), are docstrings, which document what each function does, the parameters it takes and what it returns or modifies.