Journal of the ACM (JACM)
Space-time tradeoffs for linear recursion
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
A PSPACE Complete Problem Related to a Pebble Game
Proceedings of the Fifth Colloquium on Automata, Languages and Programming
Time-space tradeoffs for computing functions, using connectivity properties of their circuits
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Upper and lower bounds on time-space tradeoffs
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
On the Relative Strength of Pebbling and Resolution
ACM Transactions on Computational Logic (TOCL)
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The pebble game on directed acyclic graphs can be used to model the space-time tradeoff behavior of a straight-line algorithm (SLA). In this game, the maximum number of pebbles used at any one time corresponds to the number of temporary registers available and is called space. The number of moves made to reach the outputs of the graph, or the time, corresponds to the number of operations required by the SLA. In this paper, it is shown that there exist infinite families of constructible graphs on N nodes which possess an extreme time-space tradeoff. For a particular set of graphs, if space is restricted to fall in the range of &THgr;(log N) to &THgr;((@@@@N/log N)), then the pebbling time necessary is superpolynomial in N. This result is obtained by deriving a lower bound on time when extra space is restricted, and then diagonalizing over the amount of this space. An extension of this argument shows that the minimum space requirement for such constructible graph families can grow as any slowly increasing function of N.