Perfect page placement

Careful page placement policies are memory management heuristics that map virtual pages to physical memory in a manner that tends to reduce the average CPU cache conflict miss rate compared to random placement. Careful placement is particularly well-suited to large direct-mapped caches. Perfect page placement is the limiting case of careful placement and is achieved by a virtual page mapping that minimizes the conflict miss rate. Cache performance curves for perfect page placement are useful benchmarks for estimating the relative error of other careful placement policies. On-line perfect placement is not realizable because the computation requires future knowledge of the memory reference string. However, off-line perfect placement is a systems modeling tool analogous to the OPT page replacement policy for virtual memory systems; both policies are tools for computing upper bounds on memory system performance. In this paper, perfect page placement is presented and proved NP-hard for demand-paged virtual memory systems with direct-mapped caches and infinite physical memory capacity. A class of perfect placement approximation algorithms is also presented and proved NP-hard.