The Wiener maximum quadratic assignment problem

Eranda Çela; Nina S. Schmuck; Shmuel Wimer; Gerhard J. Woeginger

doi:10.1016/j.disopt.2011.02.002

The Wiener maximum quadratic assignment problem

Eranda Çela
, Nina S. Schmuck
, Shmuel Wimer
, Gerhard J. Woeginger

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

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
Pages (from-to)	411-416
Number of pages	6
Journal	Discrete Optimization
Volume	8
Issue number	3
DOIs	https://doi.org/10.1016/j.disopt.2011.02.002
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
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

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10.1016/j.disopt.2011.02.002

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title = "The Wiener maximum quadratic assignment problem",

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 = "Combinatorial optimization, Computational complexity, Degree sequence, Graph theory, Wiener index",

author = "Eranda {\c C}ela and Schmuck, \{Nina S.\} and Shmuel Wimer and Woeginger, \{Gerhard J.\}",

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). ",

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doi = "10.1016/j.disopt.2011.02.002",

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AU - Wimer, Shmuel

AU - Woeginger, Gerhard J.

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N2 - 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.

AB - 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.

KW - Combinatorial optimization

KW - Computational complexity

KW - Degree sequence

KW - Graph theory

KW - Wiener index

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The Wiener maximum quadratic assignment problem

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Keywords

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