NP-completeness of maximal independent queen domination on polyominoes

A polyomino is a finite union of edge-connected unit squares in the plane. A set of queens is independent when no two queens attack each other, and it is maximal dominating when it dominates every square and no queen can be added while preserving independence.

Maximal independent queen domination conjecture. The maximal independent queen domination problem on polyominoes is NP-complete.

The conjecture asks whether the queen analogue of the known polynomial-time rook result becomes NP-complete already in dimension two. The paper reports extensive computations supporting this expectation, but no reduction is given.