Technical Report CS0794

In this paper we study positioning strategies for improving the performance of a memory system with a direct mapped cache. A positioning technique determines for every program item, instruction or data, its address in main memory. We break the general positioning problem into two, the collision minimization and the grouping problems. We show that both the mapping and the grouping problems are NP-complete and that the mapping problem is also hard to approximate. In addition, we look at probabilistic models. While in the Independent Reference Model (IRM), the optimal strategies can be found by simple polynomial algorithms [2], in the more realistic Markov model we show that the grouping problem is NP-complete.