this is funny math. MLEs. probability theory. ugh. i sort of hate it. worse, you don't want to start letting programmers do the math because the flat reality is that they're going to do it wrong.

...but i realize that there's a huge class of relatively simple practical problems that are NP and that require complete rethinks to approach.

to put it another way, the algorithm is going to have very, very bad results from time to time. so, you write in a time-out operation and start again. it's random, so you could get 100 bad results in a row. that's extreme, but it will happen from time to time. when you do get a good result, though, the guessing is often going to be faster than a systematic approach.

but, it's all guessing and working with probabilities.

http://www.sciencedaily.com/releases/2013/12/131202121546.htm