## 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.

Original language | English |
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Pages (from-to) | 411-416 |

Number of pages | 6 |

Journal | Discrete Optimization |

Volume | 8 |

Issue number | 3 |

DOIs | |

State | Published - Aug 2011 |

### Bibliographical note

Funding Information:Gerhard Woeginger acknowledges support by the Netherlands Organization for Scientific Research (NWO) , grant 639.033.403 , by DIAMANT (an NWO mathematics cluster), and by BSIK grant 03018 (BRICKS: Basic Research in Informatics for Creating the Knowledge Society).

### Funding

Gerhard Woeginger acknowledges support by the Netherlands Organization for Scientific Research (NWO) , grant 639.033.403 , by DIAMANT (an NWO mathematics cluster), and by BSIK grant 03018 (BRICKS: Basic Research in Informatics for Creating the Knowledge Society).

Funders | Funder number |
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BSIK | 03018 |

DIAMANT | |

Netherlands Organization for Scientific Research | |

Nederlandse Organisatie voor Wetenschappelijk Onderzoek | 639.033.403 |

## Keywords

- Combinatorial optimization
- Computational complexity
- Degree sequence
- Graph theory
- Wiener index