Mathematical systems theory

, Volume 16, Issue 1, pp 9–27 | Cite as

Space-time tradeoffs for linear recursion

  • Sowmitri Swamy
  • John E. Savage


A linear recursive procedure is one each of whose executions activates at most one invocation of itself. When linear recursion cannot be replaced by iteration, it is usually implemented with a stack of size proportional to the depth of recursion. In this paper we analyze implementations of linear recursion which permit large reductions in storage space at the expense of a small increase in computation time. For example, if the depth of recursion isn, storage space can be reduced to\(\sqrt n \) at the cost of a constant factor increase in running time. The problem is treated by abstracting any implementation of linear recursion as the pebbling of a simple graph, and for this abstraction we exhibit the optimal space-time tradeoffs.


Computation Time Computational Mathematic Large Reduction Constant Factor Storage Space 
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Copyright information

© Springer-Verlag New York Inc. 1983

Authors and Affiliations

  • Sowmitri Swamy
    • 1
  • John E. Savage
    • 2
  1. 1.Coordinated Science LaboratoryUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Department of Computer ScienceBrown UniversityProvidenceUSA

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