New special cases of the Quadratic Assignment Problem with diagonally structured coefficient matrices
Abstract
We consider new polynomially solvable cases of the well-known Quadratic Assignment Problem involving coefficient matrices with a special diagonal structure. By combining the new special cases with polynomially solvable special cases known in the literature we obtain a new and larger class of polynomially solvable special cases of the QAP where one of the two coefficient matrices involved is a Robinson matrix with an additional structural property: this matrix can be represented as a conic combination of cut matrices in a certain normal form. The other matrix is a conic combination of a monotone anti-Monge matrix and a down-benevolent Toeplitz matrix. We consider the recognition problem for the special class of Robinson matrices mentioned above and show that it can be solved in polynomial time.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2016
- DOI:
- 10.48550/arXiv.1609.06223
- arXiv:
- arXiv:1609.06223
- Bibcode:
- 2016arXiv160906223C
- Keywords:
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- Mathematics - Optimization and Control;
- 90C27