Lets say I have a diagram of a knot in some notation. What's the fastest algorithm to simplify it? Or asked differently: what algorithms do software usually use? I do not need to put it into the very minimal canonical form, since this is difficult to guarantee, just some form that is likely to be minimal or at least less than the original knot.

There are two methods that I can imagine: (1) program the Reidemeister moves and just keep applying them in some manner. (2) define some measure of energy and somehow gradually try to minimize it.

What I would like is to have a fast method that could process millions of complicated knots.

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