Selected topics on assignment problems
Discrete Applied Mathematics
Computers and Operations Research
A study of the quadratic semi-assignment polytope
Discrete Optimization
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The SQAP-polytope was associated to quadratic assignment problems with a certain symmetric objective function structure by Rijal (1995) and Padberg and Rijal (1996). We derive a technique for investigating the SQAP-polytope that is based on projecting the (low-dimensional) polytope into a lower dimensional vector-space, where the vertices have a "more convenient" coordinate structure. We exploit this technique in order to prove conjectures by Padberg and Rijal on the dimension of the SQAP-polytope as well as on its trivial facets.