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arXiv · 1407.2801

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

Monique Laurent·Matteo Seminaroti
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Abstract

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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Monique Laurent, Matteo Seminaroti. 2014-07-10. The quadratic assignment problem is easy for Robinsonian matrices with Toeplitz structure. https://arxiv.org/abs/1407.2801

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