Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Weak-order extensions of an order

  • Conference paper
  • First Online:
Graph-Theoretic Concepts in Computer Science (WG 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1335))

Included in the following conference series:

Abstract

In this paper, at first we describe a graph representing all the weak-order extensions of a partially ordered set and an algorithm generating them. Then we present a graph representing all of the minimal weak-order extensions of a partially ordered set, and implying a generation algorithm. Finally, we prove that the number of weak-order extensions of a partially ordered set is a comparability invariant, whereas the number of minimal weak-order extensions of a partially ordered set is not a comparability invariant.

Supported by IFP Digitale Filter.

This work was supported by the PROCOPE Program

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Birkhoff, G.Lattice Theory, 3rd ed. American Math. Soc., Providence, RI, 1967.

    Google Scholar 

  2. Bonnet, R., and Pouzet, M. Extensions et stratifications d'ensembles dispersés. C. R. Acad. Sci. 268 (1969), 1512–1515.

    Google Scholar 

  3. Bordat, J. Calcul pratique du treillis de gallois d'une correspondance. Math. Sci. Hun. 96 (1986), 31–47.

    Google Scholar 

  4. Bouchitté, V., and Habib, M. The calculation of invariants for partially ordered sets. In Algorithms and Order (1989), I. Rival, Ed., Kluwer Acad. Publ., Dordrecht, pp. 231–279.

    Google Scholar 

  5. Chretienne, P., and Carlier, J.Problèmes d'Ordonnancement. Masson, 1988.

    Google Scholar 

  6. Conway, R., Maxwell, W., and Miller, L.Theory of Scheduling. Addison-Wesley, 1967.

    Google Scholar 

  7. Dreesen, B., Poguntke, W., and Winkler, P. Comparability invariance of the fixed point property. Order 2 (1985), 269–274.

    Google Scholar 

  8. Habib, M., Morvan, M., Pouzet, M., and Rampon, J. Extensions intervallaires minimales. C. R. Acad. Sci. 318 (1991), 893–898.

    Google Scholar 

  9. Jourdan, G.-V., Rampon, J.-X., and Dard, C. Computing on-line the lattice of maximal antichains of posets. Order 11, 3 (1994), 197–210.

    Google Scholar 

  10. Lamport, L. Time, clocks, and the ordering of events in a distributed system. Communications of the ACM 21, 7 (1978), 558–565.

    Google Scholar 

  11. Möhring, R. H., and Radermacher, F. J. The order-theoretic approach to scheduling: The deterministic case. In Advances in Project Scheduling (1989), R. Slowinski and J. Weglarz, Eds., Elsevier Science Publishers B.V., Amsterdam, pp. 29–66.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LIAFA/IBP, Université Denis Diderot Paris 7, 2, place Jussieu, Case 7014, 75256, Paris Cedex 05, France

    Karell Bertet & Michel Morvan

  2. Technische Universität Berlin, Sekr. MA 6-1, D-10623, Berlin, Germany

    Jens Gustedt

Authors
  1. Karell Bertet
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jens Gustedt
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michel Morvan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Rolf H. Möhring

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bertet, K., Gustedt, J., Morvan, M. (1997). Weak-order extensions of an order. In: Möhring, R.H. (eds) Graph-Theoretic Concepts in Computer Science. WG 1997. Lecture Notes in Computer Science, vol 1335. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024488

Download citation

  • DOI: https://doi.org/10.1007/BFb0024488

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63757-8

  • Online ISBN: 978-3-540-69643-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation