Elimination of recursive calls using a small table of “randomly” selected function values

Abstract

This case study concerns the use of a table of selected function values to avoid repeated function evaluations and, particularly, to speed up recursive ones. It is assumed that the table cannot hold all repeatedly needed function values owing to storage limitations (“small-table technique”). The programmer is then faced with the problem of finding a table management policy that reduces repeat evaluations to a minimum, a problem which must usually be tackled by heuristic means. We test and discuss a spectrum of policies, most of which involve “random” selection of function values for tabulation. Savings of 95% or more are easily achieved, apparently even in the limit as the computational burden increases. Policies involving table search proper are noted to be inferior. Sometimes intuitively reasonable policy refinements fail, so efficient policy selection must be based on experiments of the kind presented here. Several other programming recommendations are made, as well as suggestions for theoretical research.