1. New special cases of the Quadratic Assignment Problem with diagonally structured coefficient matrices
- Author
-
Vladimir G. Deineko, Eranda Çela, and Gerhard J. Woeginger
- Subjects
90C27 ,Information Systems and Management ,General Computer Science ,Quadratic assignment problem ,0211 other engineering and technologies ,0102 computer and information sciences ,02 engineering and technology ,Management Science and Operations Research ,01 natural sciences ,Industrial and Manufacturing Engineering ,Combinatorics ,Sylvester's law of inertia ,Integer matrix ,Matrix (mathematics) ,Matrix splitting ,FOS: Mathematics ,Matrix analysis ,Mathematics - Optimization and Control ,Mathematics ,Discrete mathematics ,021103 operations research ,Toeplitz matrix ,Optimization and Control (math.OC) ,010201 computation theory & mathematics ,Conic section ,Modeling and Simulation - 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.
- Published
- 2018