Are there algorithms for untangling knots?

[David Carroll]

Everytime I sit down at the computer, I pull out my earbuds to plug into the harddrive so I can listen to music while I post things on PF.com...among other things :) The problem is, everytime I pull my earbuds out of my pocket, it's all tangled in a mess. My method is, I start with the plug-end and pull that out of the most simple-looking loop, then I pick the next most simple-looking loop and pull the plug-end out of that, and so forth.

I was wondering: is this the best method? Is there a mathematics that defines this sort of problem and solves it? Is there some sort of algorithm for the most efficient method of untangling knots, wires, and so forth?

 

[slider142]

Everytime I sit down at the computer, I pull out my earbuds to plug into the harddrive so I can listen to music while I post things on PF.com...among other things :) The problem is, everytime I pull my earbuds out of my pocket, it's all tangled in a mess. My method is, I start with the plug-end and pull that out of the most simple-looking loop, then I pick the next most simple-looking loop and pull the plug-end out of that, and so forth.

I was wondering: is this the best method? Is there a mathematics that defines this sort of problem and solves it? Is there some sort of algorithm for the most efficient method of untangling knots, wires, and so forth?

In knot theory, the Reidemeister moves are the only three moves sufficient to turn any representation of a knot into another representation (such as a simpler one with fewer crossings). For your purposes, where you have free ends, a few more moves are available that allow you to untangle actual knots as well. However, recognizing the Reidemeister crossings will allow you to quickly decrease the number of apparent knots in the tangle, allowing you to focus on the actual knots. Ie., a complicated looking tangle may be reduced to a simple trefoil knot with only a few moves, none of which require any motion of the ends. I haven't studied the theory in depth, but apparently the unknotting problem is still an active area of research.

 

[David Carroll]

Thank you, slider142.