The Computational Complexity of Knot and Link Problems

Authors:
Joel Hass;Jeffrey C. Lagarias;Nicholas Pippenger
Affiliations:
-;-;-
Venue:
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Year:
1997

Citing 0
Cited 3

The computational complexity of knot and link problems

Journal of the ACM (JACM)
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Linkless and flat embeddings in 3-space and the unknot problem

Proceedings of the twenty-sixth annual symposium on Computational geometry

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Abstract

We consider the problem of deciding whether a polygonal knot in 3-dimensional Euclidean space is unknotted (that is, whether it is 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 (that is, whether they are capable of being continuously deformed without self-intersection so that they occupy both sides of a plane without intersecting it), and show that it also is in NP. Finally, we show that the problem of determining the genus of a polygonal knot (a generalization of the problem of determining whether it is unknotted) is in PSPACE.