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Time-space trade-offs in a pebble game

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Summary

A certain pebble game on graphs has been studied in various contexts as a model for the time and space requirements of computations [1,2,3,8]. In this note it is shown that there exists a family of directed acyclic graphs G n and constants c 1, c 2, c 3 such that

  1. (1)

    G n has n nodes and each node in G n has indegree at most 2.

  2. (2)

    Each graph G n can be pebbled with c 1√n pebbles in n moves.

  3. (3)

    Each graph G n can also be pebbled with c 2√n pebbles, c 2<c1, but every strategy which achieves this has at least 2c 3√n moves.

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References

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  8. Sethi, R.: Complete register allocation problems. SIAM J. Comput. 4, 226–248 (1975)

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Authors and Affiliations

  1. Fakultät für Mathematik der Universität Bielefeld, D-4800, Bielefeld 1, Germany (Fed. Rep.)

    W. J. Paul

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

    R. E. Tarjan

Authors
  1. W. J. Paul
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  2. R. E. Tarjan
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Additional information

Research partially supported by DAAD (German Academic Exchange Service) Grant No. 430/402/653/5

Research partially supported by the National Science Foundation, Grant No. MCS 75-22870 and by the Office of Naval Research, Contract No. N00014-76-C-0688

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Paul, W.J., Tarjan, R.E. Time-space trade-offs in a pebble game. Acta Informatica 10, 111–115 (1978). https://doi.org/10.1007/BF00289150

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  • DOI: https://doi.org/10.1007/BF00289150

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