The Quadratic Assignment Problem is Easy for Robinsonian Matrices

  • Monique Laurent
  • Matteo Seminaroti
    • Categories Combinatorial Optimization Short URL: https://optimization-online.org/?p=12977

    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

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