The hardness of data packing

Abstract

A program can benefit from improved cache block utilization when contemporaneously accessed data elements are placed in the same memory block. This can reduce the program's memory block working set and thereby, reduce the capacity miss rate. We formally define the problem of data packing for arbitrary number of blocks in the cache and packing factor (the number of data objects fitting in a cache block) and study how well the optimal solution can be approximated for two dual problems. On the one hand, we show that the cache hit maximization problem is approximable within a constant factor, for every fixed number of blocks in the cache. On the other hand, we show that unless P=NP, the cache miss minimization problem cannot be efficiently approximated.