QAPS on Specially Structured Matrices

  • Eranda Çela
Part of the Combinatorial Optimization book series (COOP, volume 1)

Abstract

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.

Keywords

Travel Salesman Problem Travel Salesman Problem Coefficient Matrice Circulant Matrice Partial Permutation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Eranda Çela
    • 1
  1. 1.Institute of MathematicsTechnical University GrazGrazAustria

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