QAPS on Specially Structured Matrices
In this chapter and in the two next chapters we consider polynomially solvable and provably difficult (NP-hard) cases of the QAP. As there is no hope to find a polynomial time algorithm for solving the general QAP, and as QAP instances arising in different practical applications may often have a special structure, it is interesting to derive polynomial time algorithms for solving special cases of the problem. On the other hand, any information on provably difficult (NP-hard) cases of the problem is of particular relevance for a better understanding of the problem and its complexity. Nowadays there exist only few, sporadic results concerning this challenging but difficult aspect of research on the QAP. We try to give a systematic presentation of the already existing results on complexity questions related to special cases of the QAP, focusing on methodology issues. Further, we formulate a number of open problems which we consider to be a promising obj ect of further research in this direction.
KeywordsTravel Salesman Problem Travel Salesman Problem Coefficient Matrice Circulant Matrice Partial Permutation
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