Subset quadratic assignment problem

Abstract

Variants of QAP have become the hot lines in research on NP-Hard combinatorial optimization problems. There exists a new kind of problem which can't be modeled as QAP or its existing variants, in applications such as hospital layout whose facility must be assigned to one location in some predefined subset. This new problem is modeled as the subset QAP (SQAP) in this paper. We show that SQAP is NP-Hard and no ε - approximation algorithm exists for it (ε > 0). Furthermore, we prove that it can be determined in polynomial time whether a feasible solution exists or not, by proving its equivalence to perfect matching problem on bipartite graph. © 2012 Springer-Verlag.