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The quadratic assignment problem is easy for robinsonian matrices

Laurent,M.
; 
Seminaroti,M.
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 AA and BB are respectively a Robinson similarity and dissimilarity matrix and one of AA or BB 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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Date
2015-01
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Tilburg University Research Output Collection
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Keywords
quadratic assignment problem, seriation, Robinson (dis)similarity, well solvable special case
Citation
Laurent, M & Seminaroti, M 2015, 'The quadratic assignment problem is easy for robinsonian matrices', Operations Research Letters, vol. 43, no. 1, pp. 103-109. https://doi.org/10.1016/j.orl.2014.12.009
URI
https://hdl.handle.net/20.500.14602/61966
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