Quadratic assignment problems generated with the Palubetskis algorithm are degenerate

Abstract

The quadratic assignment problem (QAP) is a combinatorial optimization problem that arises in many applications such as the allocation of processes in distributed computer systems. The QAP is NP-hard and therefore no algorithms are known for solving the QAP in polynomial time. For this reason a variety of heuristic methods have been proposed for this problem. In order to evaluate heuristics, Palubetskis proposed an algorithm that generates QAPs with known optimal solution value. We show in this paper that given a Palubetskis instance (but not its optimal value) the corresponding optimal value can be determined via a linear program, polynomial in the input data, i.e., in polynomial time. This implies that problems generated by the Palubetskis method belong to a simple and degenerate subclass of QAPs and are therefore not appropriate for algorithm testing. The proof technique suggests moreover a new lower bound for Euclidean QAPs.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>