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)


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.


Bipartite Graph Directed Acyclic Graph Output Node Storage Location Input Node 
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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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