### 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.

Original language | English |
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Place of Publication | Ithaca |

Publisher | Cornell University Library |

Number of pages | 14 |

Volume | 1407.2801 |

Publication status | Published - 10 Jul 2014 |

### Publication series

Name | Preprint at arXiv |
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Volume | 1407.2801v1 |

### Keywords

- quadratic assignment problem
- Robinson (dis)similarity
- seriation
- well solvable special case

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## Cite this

Laurent, M., & Seminaroti, M. (2014).

*The Quadratic Assignment Problem is Easy for Robinsonian Matrices*. (Preprint at arXiv; Vol. 1407.2801v1). Cornell University Library. http://arxiv.org/pdf/1407.2801v1.pdf