The Class of Constraint Satisfaction Problems over a Knot

This work presents a method for associating a class of constraint satisfaction problems to a three-dimensional knot. Given a knot, one can build a knot quandle, which is a generally an infinite, free algebra. The desired collection of problems is derived from the finite quotients of the knot quandle by applying theory that relates finite algebras to constraint languages. Along the way, notions of tractable and NP-complete quandles and knots are developed. Finally, a partial, computational classification of Rolfsen’s Knot Table [26] is undertaken where it is shown that all tricolorable knots in this collection are NP-complete.