On the euclidean TSP with a permuted Van der Veen matrix

Authors:
Rainer E. Burkard;Vladimir G. Deineko
Affiliations:
TU Graz, Institut für Mathematik B, Steyrergasse 30, A-8010 Graz, Austria;The University of Warwick, Warwick Business School, Coventry CV4 7AL, UK
Venue:
Information Processing Letters
Year:
2004

Citing 2
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Abstract

We discuss the problem of recognizing permuted Van der Veen (VdV) matrices. It is well known that the TSP with a VdV matrix as distance matrix is pyramidally solvable. In this note we solve the problem of recognizing permuted strong VdV matrices. This yields an O(n4) time algorithm for the TSP with a permuted Euclidean VdV matrix. The problem, however, of recognizing permuted VdV matrices in general remains open.