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The cone of Monge matrices: Extremal rays and applications

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Abstract

We present an additive characterization of Monge matrices based on the extremal rays of the cone of nonnegative Monge matrices. By using this characterization, a simple proof for an old result by Supnick (1957) on the traveling salesman problem on Monge matrices is derived.

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References

  1. Burkard RE, Klinz B, Rudolf R (1994) Perspectives of monge properties in optimization, Report 2, SFB. Optimierung und Kontrolle. University of Technology Graz Austria, to appear in Discrete Applied Mathematics

  2. Hoffman AJ (1961) On simple linear programming problems, in Convexity Proc Symposia in Pure Mathematics AMS Providence RI 317–327

  3. Lawler EL, Lenstra JK, Rinnooy Kan AHG, Shmoys DB (1985) The traveling salesman problem. Wiley Chichester

    Google Scholar 

  4. Michalski M (1987) On a class of polynomially solvable travelling salesman problems. Zastosowania Matematyki (Applicationes Mathematicae) XIX 3–4:531–539

    Google Scholar 

  5. Monge G (1781) Mémoires sur la théorie des débais et des remblais. In Historie de l'Academie Royale des Science, Année M. DCCLXXXI, avec les Mémoires de Mathématique et de Physique, pour la même Année, Tirés des Registres de cette Académie 666–704

  6. Park JK (1991) A special case of then-vertex traveling salesman problem that can be solved inO(n) time. Information Processing Letters 40:247–254

    Google Scholar 

  7. Supnick F (1957) Extremal hamiltonian lines. Annals of Math 66:179–201

    Google Scholar 

  8. Yao FF (1982) Speed-up in dynamic programming. SIAM Journal on Algebraic and Discrete Methods 3:532–540

    Google Scholar 

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Authors and Affiliations

  1. TU Graz, Institut für Mathematik B, Steyrergasse 30, 8010, Graz, Austria

    Rüdiger Rudolf & Gerhard J. Woeginger

Authors
  1. Rüdiger Rudolf
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  2. 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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Rudolf, R., Woeginger, G.J. The cone of Monge matrices: Extremal rays and applications. ZOR - Methods and Models of Operations Research 42, 161–168 (1995). https://doi.org/10.1007/BF01415751

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  • DOI: https://doi.org/10.1007/BF01415751

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