Twist number and the alternating volume of knots

It was previously shown by the first author that every knot in S3 is ambient isotopic to one component of a two-component, alternating, hyperbolic link. In this paper, we define the alternating volume of a knot K to be the minimum volume of any link L in a natural class of alternating, hyperbolic links such that K is ambient isotopic to a component of L. Our main result shows that the alternating volume of a knot is coarsely equivalent to the twist number of a knot.