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Time-space trade-offs in a pebble game

  • W. J. Paul
  • R. E. Tarjan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 52)

Abstract

A certain pebble game on graphs has been studied in various contexts as a model for time and space requirements of computations [1,2,3,7]. In this note it is shown that there exists a family of directed acyclic graphs Gn and constants c1,c2,c3 such that
  1. 1)

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

     
  2. 2)

    Each graph Gn can be pebbled with \(c_1 \sqrt n\) pebbles in n moves.

     
  3. 3)

    Each graph Gn can also be pebbled with \(c_2 \sqrt n\) pebbles, c2 < c1,

     

but every strategy which achieves this has at least \(2^{c_3 \sqrt n }\) moves.

Keywords

Bipartite Graph Directed Acyclic Graph Output Node Storage Location Input Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    S.A. Cook: An observation on time-storage trade off Proceedings 5th ACM-STOC 1973. 29–33Google Scholar
  2. 2.
    J. Hopcroft, W. Paul and L. Valiant: On time versus space and related problems 16th IEEE-FOCS 1975, 57–64.Google Scholar
  3. 3.
    M.S. Paterson and C.E. Hewitt: Comparative schematology Record of Project MAC Conf. on Concurrent Systems and Parallel Computation 1970, 119–128Google Scholar
  4. 4.
    W.Paul, R.E. Tarjan and J.R. Celoni: Space bounds for a game on graphs 8th ACM-STOC 1976, 149–160Google Scholar
  5. 5.
    M.S. Pinsker: On the complexity of a concentrator 7th International Teletraffic Congress, Stockholm 1973Google Scholar
  6. 6.
    N. Pippenger: Superconcentrators Technical Report IBM Yorktown Heights 1976Google Scholar
  7. 7.
    R. Sethi: Complete register allocation problems Proceedings 5th ACM-STOC 1973, 182–195Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • W. J. Paul
    • 1
  • R. E. Tarjan
    • 2
  1. 1.Fakultät für Mathematik der Universität BielefeldBielefeld 1Germany
  2. 2.Computer Science DepartmentStanford UniversityStanfordUSA

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