The Wiener maximum quadratic assignment problem

Authors:
Eranda ÇEla;Nina S. Schmuck;Shmuel Wimer;Gerhard J. Woeginger
Affiliations:
Institut für Optimierung und Diskrete Mathematik, TU Graz, Steyrergasse 30, A-8010 Graz, Austria;Institut für Optimierung und Diskrete Mathematik, TU Graz, Steyrergasse 30, A-8010 Graz, Austria;School of Engineering, Bar-Ilan University, Ramat-Gan 52900, Israel;Department of Mathematics and Computer Science, TU Eindhoven, P.O.Box 513, 5600 MB Eindhoven, Netherlands
Venue:
Discrete Optimization
Year:
2011

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Abstract

We investigate a special case of the maximum quadratic assignment problem where one matrix is a product matrix and the other matrix is the distance matrix of a one-dimensional point set. We show that this special case, which we call the Wiener maximum quadratic assignment problem, is NP-hard in the ordinary sense and solvable in pseudo-polynomial time. Our approach also yields a polynomial time solution for the following problem from chemical graph theory: find a tree that maximizes the Wiener index among all trees with a prescribed degree sequence. This settles an open problem from the literature.