http://www.spoj.pl/problems/NOTOKNOT/

Wiki:

http://en.wikipedia.org/wiki/Unknotting_problem

http://en.wikipedia.org/wiki/Regina_(program)

Discuss:

http://mathoverflow.net/questions/53262/why-is-it-so-hard-to-implement-hakens-algorithm-for-knot-theory

I have try to solve this problem for more than half a month. Read all the book I can found in the local Library and I can't even find a direction !...

Is there a polynomial complexity algorithm or only have a physical simulation algorithm ? ... I was particularly interested in the matter, any one can guide me a correct direction ~~

Thanks a lot!..