On the power of white pebbles

Abstract

We construct a family (G p |p) of directed acyclic graphs such that any black pebble strategy forG p requiresp 2 pebbles whereas 3p+1 pebbles are sufficient when white pebbles are allowed.

This is a preview of subscription content, access via your institution.

References

  1. [1]

    S. A. Cook, andR. Sethi: Storage requirements for deterministic polynomial finite recognizable languages,J. Comput. Syst. Sci., Vol.13, pp. 25–37, 1976.

    Google Scholar 

  2. [2]

    C. E. Hewitt, andM. S. Paterson: Comparative schematology,Project MAC conf. on Concurrent Systems and Parallel Computation, Woods Hole, pp. 119–127, 1970.

  3. [3]

    M. M. Klawe: A tight bound for black and white pebbles on the pyramid,J. ACM, Vol.32, No. 1, pp. 218–228, January 1985.

    Google Scholar 

  4. [4]

    T. Lengauer, R. Tarjan: Asymptotically tight bounds on time-space trade-offs in a pebble game,J. ACM, Vol.29, No. 4, pp. 1087–1130, October 1982.

    Google Scholar 

  5. [5]

    F. Meyer auf der Heide: A comparison of two variations of a pebble game on graphs,Theoretical Computer Science, Vol.13, pp. 315–322, 1981.

    Google Scholar 

  6. [6]

    N. Pippenger: Pebbling,IBM Research Report RC8258, 1980.

  7. [7]

    W. J. Savitch: Relationship between Nondeterministic and Deterministic Tape Complexities,J. Comp. and Sys. Sci., Vol.4, pp. 177–192, 1980.

    Google Scholar 

  8. [8]

    R. Wilber: White pebbles help,J. Comput. Syst. Sci., Vol.36, pp. 108–124, 1988.

    Google Scholar 

  9. [9]

    R. Wilber: A comparison of the Black and Black-White Pebble Games,Doctoral Thesis, Carnegie-Mellon University,1985.

Download references

Author information

Affiliations

Authors

Additional information

Supported by the National Science Foundation under contract no. DCR-8407256 and by the office of Naval Research under contract no. N0014-80-0517.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Kalyanasundaram, B., Schnitger, G. On the power of white pebbles. Combinatorica 11, 157–171 (1991). https://doi.org/10.1007/BF01206359

Download citation

AMS subject classification (1980)

  • 68 Q 05
  • 68 R 05
  • 68 R 10