The Implementer’s Dilemma: A Mathematical Model of Compile Time Garbage Collection

Abstract

Optimization by compile time garbage collection is one possible weapon in the functional language implementer’s armoury for combatting the excessive memory allocation usually exhibited by functional programs. It is an interesting idea, but the practical question of whether it yields benefits in practice has still not been answered convincingly one way or the other.

In this short paper we present a mathematical model of the performance of straightforward versions of mark-scan and copying garbage collectors with programs optimized for explicit deallocation. A mark-scan heap manager has a free list, whereas a copying heap manager does not — herein lies the dilemma, since a copying garbage collector is usually considered to be faster than a mark-scan, but it cannot take advantage of this important optimization.

For tract ability we consider only heaps with fixed cells. The results reported show that the garbage collection scheme of choice depends quite strongly on the heap occupancy ratio: the proportion of the total heap occupied by accessible data structures averaged over the execution of the program. We do not know what typical heap occupancy ratios are, and so are unable to make specific recommendations, but the results may be of use in tailoring applications and heap management schemes, or in controlling schemes where the heap size varies dynamically.

An important result arising from the work reported here is that when optimizing for explicit deallocation, a very large proportion of cell releases must be optimized before very much performance benefit is obtained.