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.

Original language | English |
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Publisher | s.n. |
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Number of pages | 11 |
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Publication status | Published - 2011 |
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Name | arXiv.org [math.OC] |
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Volume | 1102.3030 |
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