Abstract
The Linear-Scan algorithm (1970), applicable to priority replacement policies, computes stack distances and the number of misses incurred on a given address trace, for all cache sizes, in time O(V) per access. Here, V is the number of distinct (virtual) items referenced within the trace. While the time bound was subsequently lowered to O(log V) for the Least Recently Used policy, no improvements have been reported for general priority policies. This work introduces the class of policies with nearly static priorities (NSP), which encompasses several known policies. The Min-Tree algorithm is proposed for NSP policies, whose performance is quite sensitive to the policy as well as to the address trace. Under suitable probabilistic assumptions, the expected time per access is O(log2V). Experimental evidence collected on a mix of 30 benchmarks shows that the Min-Tree algorithm can be significantly faster than Linear-Scan, for interesting policies such as OPT (or Belady), Least Frequently Used (LFU), and Most Recently Used (MRU). Min-Tree can be parallelized to run in time O(log V) using O(V/log V) processors, in the worst case. A more sophisticated Lazy Min-Tree algorithm is also developed with \({O(\sqrt{V}\log V)}\) worst-case time per access. This bound applies, in particular, to the policies OPT, LFU, and Least Recently/Frequently Used (LRFU), for which the best previously known bound was O(V). Although random replacement is not an NSP policy, the framework developed in this work leads to a stack-distance algorithm with O(log V) expected time per access.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.