The QAP-polytope and the star transformation

The quadratic assignment problem (QAP) maybe was for a long time the one among the prominent NP-hard combinatorial optimization problems about which the fewest polyhedral results had been known. Recent work of Rijal (1995) and Padberg and Rijal (1996) has on the one hand yielded some basic facts about the associated quadratic assignment polytope, but has on the other hand shown that \naive" investigations even of the very basic questions (like the dimension, the aane hull, and the trivial facets) soon become extremely complicated. In this paper, we propose an isomorphic transformation of the \natural" realization of the quadratic assignment polytope, which simpliies the polyhedral investigations enormously. We demonstrate this by giving short proofs of the basic results on the polytope that indicate that exploiting the techniques developed in this paper deeper polyhedral investigations of the QAP now become possible. Moreover, an \inductive construction" of the QAP-Polytope is derived that might be useful in branch-and-cut algorithms.