This answer is assuming you want to sacrifice collision resistance for length (seems dubious for anything that needs to be highly reliable) and that you don't want to use auto-incrementing. Assuming your UUIDs are sufficiently random, isn't this just a generalized birthday problem? Take the birthday problem and generalize the formula from 365 buckets to N buckets, where N is the total number of possible UUIDs given a length and set of possible characters. https://mste.illinois.edu/courses/mat764fa03/folders/edwards...

You should be concerned with what happens if there's a duplicate -- you can calculate the probability of that occurring as long as you know the potential size of your dataset and set your UUID length accordingly.