The rank-genus conjecture for knot complements

For a knot $K\subset S^3$, let $r(K)$ be the minimal number of generators of $\pi_1(S^3-K)$, and let $E(K,S^3)$ denote its exterior. The rank-genus conjecture. For all knots $K\subset S^3$,

$$r(K)=g(E(K,S^3))=t(K)+1.$$

This conjecture compares the rank of a knot group with the Heegaard genus and tunnel number of its complement. The supplied source states it but provides no evidence of a resolution, so its status remains open.