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Minimal representation of semiorders with intervals of same length

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Orders, Algorithms, and Applications (ORDAL 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 831))

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Abstract

Semiorders are special interval orders which allow a representation with intervals of same length. Using integer endpoints we present here such a representation with minimal interval length.

The algorithm obtained is linear in time and space. In addition, we give a characterization of the subclass of semiorders representable by intervals of length k by a set of C k+1 forbidden suborders where C n is n-th Catalan number.

Supported by a postdoctoral fellowship of the Deutsche Forschungsgemeinschaft.

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References

  1. A. von Arnim and C. de la Higuera. Computing the jump number on semi-orders is polynomial. Discrete Applied Mathematics, 1993. To appear.

    Google Scholar 

  2. P. Baldy and M. Morvan. A linear time and space algorithm to recognize interval orders. Discrete Applied Mathematics, 46:173–178, 1993.

    Google Scholar 

  3. K. P. Bogart. A discrete proof of the Scott-Suppes representation theorem of semiorders. Technical Report PMA-TR91-173, Dartmouth College, Hanover, New Hampshire 03755, 1991. Accepted for publication in Discrete Applied Mathematics.

    Google Scholar 

  4. K. P. Bogart and K. Stellpflug. Discrete representation theory of semiorders. Accepted for publication in Discrete Applied Mathematics.

    Google Scholar 

  5. G. Brightwell. Semiorders and the 1/3–2/3 conjecture. Order, 5:369–380, 1989.

    Google Scholar 

  6. G. Brightwell and P. Winkler. Counting linear extensions is #P-complete. In Proc. 23rd ACM Symposium on the Theory of Computing, pages 175–181, 1991.

    Google Scholar 

  7. P.C. Fishburn. Interval orders and interval graphs. Wiley, New York, 1985.

    Google Scholar 

  8. R. L. Graham, D. E. Knuth, and O. Patashnik. Concrete Mathematics: a foundation of computer science. Addison-Wesley Publishing Company, Reading, Massachusetts, 1989.

    Google Scholar 

  9. J. Mitas. Tackling the jump number of interval orders. Order, 8:115–132, 1991.

    Google Scholar 

  10. M. Pirlot. Minimal representation of a semiorder. Theory and Decision, 28:109–141, 1990.

    Google Scholar 

  11. I. Rabinovitch. The dimension of semiorders. J. of Combinatorial Theory A, 25:50–61, 1978.

    Google Scholar 

  12. I. Rabinovitch. An upper bound on the dimension of interval orders. J. of Combinatorial Theory A, 25:68–71, 1978.

    Google Scholar 

  13. D. Scott and P. Suppes. Foundational aspects of theories of measurement. Journal of Symbolic Logic, 23:113–128, 1958.

    Google Scholar 

  14. R. L. Wine and J. E. Freund. On the enumeration of decision patterns involving n means. Annals of Mathematical Statistics, 28:256–259, 1957.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), 161 Rue Ada, F-34392, Montpellier Cedex 5, France

    Jutta Mitas

  2. TH Darmstadt, Fachbereich Mathematik, D-64289, Darmstadt, Germany

    Jutta Mitas

Authors
  1. Jutta Mitas
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Editor information

Vincent Bouchitté Michel Morvan

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© 1994 Springer-Verlag Berlin Heidelberg

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Mitas, J. (1994). Minimal representation of semiorders with intervals of same length. In: Bouchitté, V., Morvan, M. (eds) Orders, Algorithms, and Applications. ORDAL 1994. Lecture Notes in Computer Science, vol 831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0019433

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  • DOI: https://doi.org/10.1007/BFb0019433

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58274-8

  • Online ISBN: 978-3-540-48597-1

  • eBook Packages: Springer Book Archive

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