Many of those algorithms will require large amounts of computing power and memory. A basic Arduino like Nano 3 or Uno will not be capable of running them quickly enough, or not capable at all. So choosing your microcontroller wisely is important.
If I were building a micro mouse, and I have wanted to build one for many years, I might choose a Raspberry Pi Zero.
I don't think that any wireless/RF capability would be allowed in a contest, but could be very useful during development and testing, so I might choose a Zero W for development, which I could then swap for a Zero (non-W) during a contest.
An RPi is not an Arduino, of course. So if it must be an Arduino or Arduino compatible, then a Teensy 4.0 has similar processing power and memory.