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On the recognition of permuted Supnick and incomplete Monge matrices

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Abstract

Incomplete Monge matrices are a generalization of standard Monge matrices: the values of some entries are not specified and the Monge property only must hold for all specified entries. We derive several combinatorial properties of incomplete Monge matrices and prove that the problem of recognizingpermuted incomplete Monge matrices is NP-complete. For the special case of permutedSupnick matrices, we derive a fast recognition algorithm and thereby identify a special case of then-vertex travelling salesman problem which can be solved inO(n 2logn) time.

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Authors and Affiliations

  1. Dnepropetrovsk University, Gagarin Av. 72, Dnepropetrovsk, Ukraine

    Vladimir Deineko

  2. Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010, Graz, Austria

    Rüdiger Rudolf & Gerhard J. Woeginger

Authors
  1. Vladimir Deineko
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  2. Rüdiger Rudolf
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  3. Gerhard J. Woeginger
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Additional information

This research has been supported by the Spezialforschungsbereich F 003 “Optimierung und Kontrolle”, Projektbereich Diskrete Optimierung

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Deineko, V., Rudolf, R. & Woeginger, G.J. On the recognition of permuted Supnick and incomplete Monge matrices. Acta Informatica 33, 559–569 (1996). https://doi.org/10.1007/BF03036463

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