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The Quadratic Assignment Problem is Easy for Robinsonian Matrices

Monique Laurent(M.Laurent***at***cwi.nl)
Matteo Seminaroti(M.Seminaroti***at***cwi.nl)

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

Keywords: Quadratic Assignment Problem;Robinson (dis)similarity;seriation;well solvable special case

Category 1: Combinatorial Optimization

Citation:

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Entry Submitted: 07/11/2014
Entry Accepted: 07/28/2014
Entry Last Modified: 07/11/2014

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