  Many polynomial invariants of knots and links, including the Jones and
HOMFLY-PT polynomials, are widely used in practice but #P-hard to compute. It
was shown by Makowsky in 2001 that computing the Jones polynomial is
fixed-parameter tractable in the treewidth of the link diagram, but the
parameterised complexity of the more powerful HOMFLY-PT polynomial remained an
open problem. Here we show that computing HOMFLY-PT is fixed-parameter
tractable in the treewidth, and we give the first sub-exponential time
algorithm to compute it for arbitrary links.
