Polyhedral Methods for the QAP

  • Volker Kaibel
Part of the Combinatorial Optimization book series (COOP, volume 7)


For many combinatorial optimization problems investigations of associated polyhedra have led to enormous successes with respect to both theoretical insights into the structures of the problems as well as to their algorithmic solvability. Among these problems are quite prominent NP-hard ones, like, e.g., the traveling salesman problem, the stable set problem, or the maximum cut problem. In this chapter we overview the polyhedral work that has been done on the quadratic assignment problem (QAP). Our treatment includes a brief introduction to the methods of polyhedral combinatorics in general, descriptions of the most important polyhedral results that are known about the QAP, explanations of the techniques that are used to prove such results, and a discussion of the practical results obtained by cutting plane algorithms that exploit the polyhedral knowledge. We close by some remarks on the perspectives of this kind of approach to the QAP.


Assignment Problem Combinatorial Optimization Problem Quadratic Assignment Problem Incidence Vector Linear Description 
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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Volker Kaibel
    • 1
  1. 1.Fachbereich Mathematik, Sekr. 7-1Technische Universität BerlinBerlinGermany

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