English

The Wiener maximum quadratic assignment problem

Optimization and Control 2011-04-21 v3

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.

Keywords

Cite

@article{arxiv.1102.3030,
  title  = {The Wiener maximum quadratic assignment problem},
  author = {Eranda Çela and Nina S. Schmuck and Shmuel Wimer and Gerhard J. Woeginger},
  journal= {arXiv preprint arXiv:1102.3030},
  year   = {2011}
}

Comments

11 pages, no figures

R2 v1 2026-06-21T17:26:27.337Z