Computational complexity of the minimum queen domination problem

Determine whether the minimum queen domination problem on square chessboards is NP-hard and establish its exact complexity class.

Background

The paper distinguishes theoretical research on queen domination from computational efforts that determine optimal domination numbers and enumerate minimum dominating sets. Although prior theoretical studies have established upper and lower bounds for the number of queens required, the computational complexity of the underlying problem has not been settled. Specifically, the paper identifies both the NP-hardness question and the exact complexity classification as unresolved, leaving open the task of placing the problem within an appropriate complexity class.