New lower bounds for the quadratic assignment problem QAP are presented. These bounds are based on the orthogonal relaxation of QAP. The additional improvement is obtained by making eecient use of a tractable representation of orthogonal matrices having constant row and column sums. The new bound is easy to implement and often provides high quality bounds under an acceptable computational eeort.

It is the purpose of this paper to propose and discuss certain modifications of the ideas concerning GromovHausdorff distances in order to tackle the problems of shape matching and comparison. These reformulations render these distances more amenable to practical computations without sacrificing theoretical underpinnings. A second goal of this paper is to establish links to several other practi...

We give a (1 − 1/e)-approximation algorithm for the Max-Profit Generalized Assignment Problem (Max-GAP) with fixed profits when the profit (but not necessarily the size) of every item is independent from the bin it is assigned to. The previously best known approximation ratio for this problem was 1/2. Key-words. Generalized assignment, Approximation algorithm.

We consider semidefinite programming relaxations of the quadratic assignment problem, and show how to exploit group symmetry in the problem data. Thus we are able to compute the best known lower bounds for several instances of quadratic assignment problems from the problem library: [R.E. Burkard, S.E. Karisch, F. Rendl. QAPLIB — a quadratic assignment problem library. Journal on Global Optimiza...