Dual Robinson–Schensted–Knuth correspondence ($M⟷(T,U),T,U^t\text{ semistandard}$)

For a finite $0$-$1$ matrix, list its occupied pairs by increasing top entry and decreasing bottom entry within a top-entry tie. Perform ordinary semistandard row insertion on the bottom entries and record top entries in the new cells. The result is a bijection with same-shape tableaux $T,U$ for which $T$ and $U^t$ are Semistandard Young tableaux. The types of $T$ and $U$ are respectively the column-sum and row-sum vectors of the matrix.