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 A and B are respectively a Robinson similarity and dissimilarity matrix and one of A or B 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.
quadratic assignment, polynomial time algorithm, Robinson matrix, seriation problem
Logistics (theme 3)
North-Holland
Operations Research Letters
Mixed-Integer Nonlinear Optimization
Published paper: DOI: 10.1016/j.orl.2014.12.009
This work was funded by the European Commission 7th Framework Programme; grant id h2020/764759 - Mixed-Integer Non-Linear Optimisation Applications (MINOA)
Networks and Optimization

Laurent, M, & Seminaroti, M. (2014). The quadratic assignment problem is easy for Robinsonian matrices with Toeplitz structure. Operations Research Letters, available onlin(18 December 2014).