Eigenvalue Bounds Versus Semidefinite Relaxations for the Quadratic Assignment Problem

It was recently demonstrated that a well-known eigenvalue bound for the Quadratic Assignment Problem (QAP) actually corresponds to a semideenite programming (SDP) relaxation. However, for this bound to be computationally useful the assignment constraints of the QAP must rst be eliminated, and the bound then applied to a lower-dimensional problem. The resulting \projected eigenvalue bound" is one of the best available bounds for the QAP, especially when considering the quality of bounds relative to the complexity of obtaining them. In this paper we show that the projected eigenvalue bound also corresponds to an SDP relaxation of the original QAP.