On types of randomized algorithms

There is more than Monte Carlo when talking about randomized algorithms. It is not uncommon to see the expresions “Monte Carlo Approach” and “randomized approach” used interchangeably. More than once you start reading a paper or listening to a presentation, in which the words “Monte Carlo” appear on the keywords and even on the title, and as you keep reading/listening, you notice in the algorithm description a part in which the runs with incorrect outputs are discarded until only correct outputs are given… Which effectively turns a Monte Carlo into a Las Vegas. Running time is no longer deterministic-ish, and the algorithm will only provide correct answers. So, they say/write “Monte Carlo” here, “Monte Carlo” there, and when it comes to what actually happens, you are not really in Monte Carlo, and you might be in Vegas, baby.

You can do a small check yourself. Use your favorite search engine with “monte carlo simulation” and “las vegas simulation”. Depending on your search engine, you may get something looking more or less like this:
aprox 84 200 000 results (0,32 seconds) – monte carlo simulation

aprox   9 560 000 results (0,56 seconds) – las vegas simulation

Almost a whole order of magnitude more in relevant results from Monte Carlo, in almost half the time. Now, if you used something like google, you may or may not get relevant results in your first screen, depending on how well google knows you. Of course, there are the cases of “monte carlo simulation” that most likely refer to other topics e.g. Monte Carlo integration and the like, the same with “las vegas simulation“. And depending on how much your search engine knows your habits, you might not get any results of Las Vegas simulations right away.

And probably the next thing you may do, is to do a quick wikipedia search of “Las Vegas algorithm”. You may possibly read it, and find in the end “Atlantic City algorithm”. And maybe you may want to follow that little wikipedia rabbit hole, and end up reading about it. And then no one can save you.


The featured image in this post is from here.


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