Technical Report CIS9605

Title: Trivial or Knot: a Software Tool and Algorithms for Knot Simplification
Authors: D. Lewin, O. Gan and A.M. Bruckstein
Abstract: A special type of representation for knots and for local manipulations is described and used in a software tool called tok to implement a number of algorithms on knots. Two algorithms for knot simplification are described: simulated annealing applied to the knot representation, and a "divide-simplify-join" algorithm. Both of these algorithms make use of the compact knot representation and of the basic mechanism tok provides for carrying out a predefined knot manipulation on the knot representation. The simplification algorithms implemented with the tok system exploit local knot manipulations and have proven themselves effective for simplifying even very complicated knots in reasonable time.
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