The quadratic assignment problem is easy for Robinsonian matrices with Toeplitz structure

We present a new polynomially solvable case of the Quadratic Assignment Problem in Koopmans–Beckman form QAP(A,B), by showing that the identity permutation is optimal when AA and BB are respectively a Robinson similarity and dissimilarity matrix and one of AA or BB is a Toeplitz matrix. A Robinson (dis)similarity matrix is a symmetric matrix whose entries (increase) decrease monotonically along rows and columns when moving away from the diagonal, and such matrices arise in the classical seriation problem.