The Wiener maximum quadratic assignment problem

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. Keywords. Combinatorial optimization; computational complexity; graph theory; degree sequence; Wiener index.

• Type: Journal
• Year: 2011
• Where: DISOPT
• Authors: Eranda Çela, Nina S. Schmuck, Shmuel Wimer, Gerhard J. Woeginger
• Keywords: Computer Networks, DISOPT 2011, Polynomial Time Solution, Pseudo Polynomial, Quadratic Assignment Problem