Skip to main content
SpringerLink
Log in

Two processor scheduling is in NC

  • Conference paper
  • First Online:
VLSI Algorithms and Architectures (AWOC 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 227))

Included in the following conference series:

Abstract

We present a parallel algorithm for the two processor scheduling problem. This algorithm constructs an optimal schedule for unit execution time task systems with arbitrary precedence constraints using a polynomial number of processors and running in time polylog in the size of the input. Whereas previous parallel solutions for the problem made extensive use of randomization, our algorithm is completely deterministic and based on an interesting iteration technique. It is of independent relevance for two more reasons. It provides another example for the apparent difference in complexity between decision and search problems in the context of fast parallel computation, and it gives an NC-algorithm for the matching problem in certain restricted cases.

This work was supported in part by a grant from AT&T Foundation, ONR contract N00014-85-C-0731, and NSF grant DCR-8351757.

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.

Similar content being viewed by others

References

  1. Coffman, E.G., Jr., and R.L. Graham “Optimal Scheduling for Two Processor Systems," Acta Informatica 1 (1972), pp. 200–213.

    Google Scholar 

  2. Dolev, D., E. Upfal, and M. Warmuth, “Scheduling Trees in Parallel,” In: Bertolazzi, P, Luccio, F. (eds.): VLSI: Algorithms and Architectures. Proceedings of the of the International Workshop on Parallel Computating and VLSI, Amalfi, Italy (May 1984): North-Holland 1985, p. 1–30.

    Google Scholar 

  3. Fujii, M., T. Kasami, and K. Ninamiya, “Optimal Sequencing of Two Equivalent Processors," SIAM J. of Computing 17 (1969), pp. 784–789.

    Google Scholar 

  4. Gabow, H.N., “An Almost-linear Algorithm for Two-processor Scheduling,” J.ACM 29,3 (1982), pp. 766–780.

    Google Scholar 

  5. Gabow, H.N. and Tarjan, R.E., “A Linear Time Algorithm for a Special Case of Disjoint Set Union”, Proceedings of the 15th Ann. ACM Symposium on Theory of Computing (Boston, Mass., 1983), pp. 246–251.

    Google Scholar 

  6. Ghouilà-Houri, A., “Charactérisation des graphes non orientés dont on peut orienter les arrêtes de manière à obtenir le graphe d'une relation d'ordre,” C.R. Acad. Sci. Paris 254 (1962).

    Google Scholar 

  7. Helmbold, D. and E. Mayr, “Fast Scheduling Algorithms on Parallel Computers,” STAN-CS-84-1025, Department of Computer Science, Stanford University (November 1984). To appear in Advances in Computing Research.

    Google Scholar 

  8. Helmbold, D. and E. Mayr, “Transitive Orientation and NC Algorithms,” in preparation.

    Google Scholar 

  9. Hu, T.C., “Parallel Sequencing and Assembly Line Problems,” Operations Research 9 (1961), pp. 841–848.

    Google Scholar 

  10. Karp, R.M., E. Upfal, and A. Wigderson, “Constructing a Perfect Matching is in Random NC,” Proceedings of the 17th Ann. ACM Symposium on Theory of Computing (Providence, RI, 1985), pp. 22–32.

    Google Scholar 

  11. Karp, R.M., E. Upfal, and A. Wigderson, “Are Search and Decision Problems Computationally Equivalent?,” Proceedings of the 17th Ann. ACM Symposium on Theory of Computing (Providence, RI, 1985), pp. 464–475.

    Google Scholar 

  12. Kozen, D., U.V. Vazirani, and V.V. Vazirani, “NC Algorithms for Comparability Graphs, Interval Graphs, and Testing for Unique Perfect Matching,” to appear.

    Google Scholar 

  13. Papadimitriou, C.H. and Yannakakis, M., “Scheduling Interval-Ordered Tasks,” SIAM J. Computing 8,3 (1979).

    Google Scholar 

  14. Pnueli, A., A. Lempel, and S. Even, “Transitive Orientation of Graphs and Identification of Permutation Graphs,” Can. J. Math. 23,1 (1971), pp. 160–175.

    Google Scholar 

  15. Ullman, J.D., “NP-complete Scheduling Problems," J. Comput. System Sci. 10 (1975), pp. 384–393.

    Google Scholar 

  16. Vazirani, U.V. and V.V. Vazirani, “The Two-Processor Scheduling Problem is in RNC,” Proceedings of the 17th Ann. ACM Symposium on Theory of Computing (Providence, RI, 1985), pp. 11–21.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Stanford University, USA

    David Helmbold & Ernst Mayr

Authors
  1. David Helmbold
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ernst Mayr
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Filia Makedon Kurt Mehlhorn T. Papatheodorou P. Spirakis

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Helmbold, D., Mayr, E. (1986). Two processor scheduling is in NC . In: Makedon, F., Mehlhorn, K., Papatheodorou, T., Spirakis, P. (eds) VLSI Algorithms and Architectures. AWOC 1986. Lecture Notes in Computer Science, vol 227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16766-8_2

Download citation

  • DOI: https://doi.org/10.1007/3-540-16766-8_2

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16766-2

  • Online ISBN: 978-3-540-38746-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation