Space-time tradeoffs for linear recursion

  • Authors:
  • Sowmitri Swamy;John E. Savage

  • Affiliations:
  • University of Illinois, Urbana, Illinois;Brown University, Providence, Rhode Island

  • Venue:
  • POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
  • Year:
  • 1979

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Abstract

A linear recursive procedure is one in which a procedural call can activate at most one other procedural call. 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 is n, storage space can be reduced to √n at the cost of a constant factor increase in running time. The problem is treated by abstracting linear recursion into the pebbling of a simple graph and for this abstraction we exhibit the optimal space-time tradeoffs.