The Computational Complexity of Knot and Link Problems

The Computational Complexity of Knot and Link Problems (1997)

by Joel Hass , Jeffrey C. Lagarias

Citations:

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Datum	Value	Source
TITLE	The Computational Complexity of Knot and Link Problems	user correction - Legacy Corrections
AUTHOR NAME	Joel Hass	SVM HeaderParse 0.1
AUTHOR NAME	Jeffrey C. Lagarias	SVM HeaderParse 0.1
ABSTRACT	We consider the problem of deciding whether a polygonal knot in 3dimensional Euclidean space is unknotted, 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 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. We also give exponential worstcase running time bounds for deterministic algorithms to solve each of these problems. These algorithms are based on the use of normal surfaces and decision procedures due to W. Haken, with recent extensions by W. Jaco and J. L. Tollefson. Keywords: knot theory, three-dimensional topolog...	user correction - Legacy Corrections
YEAR	1997	user correction - Legacy Corrections
CITATIONS	43 found	ParsCit 1.0