On the Euclidean TSP with a permuted Van der Veen matrix

On the Euclidean TSP with a permuted Van der Veen matrix

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( n 4) time algorithm for the TSP wit...

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Veröffentlicht in:Information processing letters 2004-09, Vol.91 (6), p.259-262
Hauptverfasser: Burkard, Rainer E, Deineko, Vladimir G
Format: Artikel
Sprache:eng
Schlagworte:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Computer science
control theory
systems
Exact sciences and technology
Matrix
Pyramidally solvable case
Studies
Theoretical computing
Traveling salesman problem
Van der Veen matrix
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Zusammenfassung: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( n 4) time algorithm for the TSP with a permuted Euclidean VdV matrix. The problem, however, of recognizing permuted VdV matrices in general remains open.
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2004.05.011