A solvable case of the quadratic assignment problem11This research has been supported by the Spezialforschungsbereich F 003 ``Optimierung und Kontrolle", Projektbereich Diskrete Optimierung.

Authors:
Vladimir G De}ıNeko;Gerhard J Woeginger
Affiliations:
Institut für Mathematik B, TU Graz, Steyrergasse 30, A-8010 Graz, Austria;Institut für Mathematik B, TU Graz, Steyrergasse 30, A-8010 Graz, Austria
Venue:
Operations Research Letters
Year:
1998

Citing 3
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The Wiener maximum quadratic assignment problem

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The three-dimensional matching problem in Kalmanson matrices

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Abstract

This short note investigates a restricted version of the quadratic assignment problem (QAP), where one of the coefficient matrices is a Kalmanson matrix, and where the other coefficient matrix is a symmetric circulant matrix that is generated by a decreasing function. This restricted version is called the Kalmanson-circulant QAP. We prove that - in strong contrast to the general QAP - this version can be solved easily. Our result naturally generalizes a well-known theorem of Kalmanson on the travelling salesman problem.