The Computational Complexity of Knot and Link Problems

@article{Hass1999TheCC,
  title={The Computational Complexity of Knot and Link Problems},
  author={Joel Hass and Jeffrey C. Lagarias and Nicholas Pippenger},
  journal={J. ACM},
  year={1999},
  volume={46},
  pages={185-211}
}
We consider the problem of deciding whether a polygonal knot in 3-dimensional Euclidean space is unknotted, ie., capable of being continuously deformed without self-intersection so that it lies in a plane. We show that this problem, UNKNOTTING PROBLEM is in NP. We also consider the problem, SPLITTING PROBLEM of determining whether two or more such polygons can be split, or continuously deformed without self-intersection so that they occupy both sides of a plane without intersecting it. We show… CONTINUE READING