A solvable case of the quadratic assignment problem

This short note investigates a restricted version of the quadratic assignment problem (QAP), where one of the coefficient matrices is a Kalmanson matrix, and where the other coefficient matrix is a symmetric circulant matrix that is generated by a decreasing function. This restricted version is called the Kalmanson-circulant QAP. We prove that – in strong contrast to the general QAP – this version can be solved easily. Our result naturally generalizes a well-known theorem of Kalmanson on the travelling salesman problem.