We investigate special cases of the quadratic assignment problem (QAP) where one of the two underlying matrices carries a simple block structure. For the special case where the second underlying matrix is a monotone anti-Monge matrix, we derive a polynomial time result for a certain class of cut problems. For the special case where the second underlying matrix is a product matrix, we identify two sets of conditions on the block structure that make this QAP polynomially solvable and NP-hard, respectively.
Çela, E., Deineko, V. G., & Woeginger, G. J. (2015). Well-solvable cases of the QAP with block-structured matrices. Discrete Applied Mathematics, 186(1), 56–65. https://doi.org/10.1016/j.dam.2015.01.005