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Space bounds for a game on graphs

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Abstract

We study a one-person game played by placing pebbles, according to certain rules, on the vertices of a directed graph. In [3] it was shown that for each graph withn vertices and maximum in-degreed, there is a pebbling strategy which requires at mostc(d) n/logn pebbles. Here we show that this bound is tight to within a constant factor. We also analyze a variety of pebbling algorithms, including one which achieves the 0(n/logn) bound.

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References

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Author notes

  1. Wolfgang J. Paul

    Present address: Faculty of Mathematics, University of Bielefeld, W. Germany

Authors and Affiliations

  1. Computer Science Department, Cornell University, 14850, Ithaca, New York, USA

    Wolfgang J. Paul

  2. Computer Science Department, Stanford University, 94305, Stanford, California, USA

    Robert Endre Tarjan & James R. Celoni

Authors
  1. Wolfgang J. Paul
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  2. Robert Endre Tarjan
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  3. James R. Celoni
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Additional information

Research partially supported by DAAD (German Academic Exchange Service) Grant No. 430/402/563/5 (W.J.P.)

Research partially supported by National Science Foundation grant MCS75-22870 and Office of Naval Research contract N0014-76-C-0688 (R.E.T. and J.R.C.).

Reproduction in whole or in part is permitted for any purpose of the United States Government.

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Paul, W.J., Tarjan, R.E. & Celoni, J.R. Space bounds for a game on graphs. Math. Systems Theory 10, 239–251 (1976). https://doi.org/10.1007/BF01683275

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  • DOI: https://doi.org/10.1007/BF01683275

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