  Given a prime, alternating link diagram, we build a special cover of the link
complement whose degree is bounded by a factorial function of the crossing
number. It follows that a subgroup of the link group of that index embeds into
right-angled Artin and Coxeter groups. Corollaries of this result include a
quantification of residual finiteness, control of the growth of Betti numbers
in covers, and an explicit bound on the rank of a Z-module on which the link
group acts faithfully.
