NP-completeness of minimal queen domination on convex polyominoes

A polyomino is a finite union of edge-connected unit squares in the plane. It is convex if every row and every column has at most one connected component. The minimal domination problem asks for the smallest attacking or non-attacking queen set that dominates the polyomino.

Convex-polyomino queen domination conjecture. The minimal domination problem for attacking, or non-attacking, queens on convex polyominoes is NP-complete.

The conjecture extends the proposed rook result to queens. The paper gives no algorithm or reduction establishing NP-completeness, so the problem remains open.