# Locality

## TL;DR

This paper proves that cache-oblivious algorithms that are asymptotically optimal in an ideal model are also optimal across various real-world systems that benefit from data locality, despite architectural differences.

## Contribution

It establishes that cache-oblivious algorithms are asymptotically optimal in any system that rewards locality of reference, broadening their applicability.

## Key findings

- Cache-oblivious algorithms are asymptotically optimal in real systems.
- Optimality holds across systems with different cache architectures.
- The result excludes some pathological cases.

## Abstract

The program performance on modern hardware is characterized by \emph{locality of reference}, that is, it is faster to access data that is close in address space to data that has been accessed recently than data in a random location. This is due to many architectural features including caches, prefetching, virtual address translation and the physical properties of a hard disk drive; attempting to model all the components that constitute the performance of a modern machine is impossible, especially for general algorithm design purposes. What if one could prove an algorithm is asymptotically optimal on all systems that reward locality of reference, no matter how it manifests itself within reasonable limits? We show that this is possible, and that excluding some pathological cases, cache-oblivious algorithms that are asymptotically optimal in the ideal-cache model are asymptotically optimal in any reasonable setting that rewards locality of reference. This is surprising as the cache-oblivious framework envisions a particular architectural model involving blocked memory transfer into a multi-level hierarchy of caches of varying sizes, and was not designed to directly model locality-of-reference correlated performance.