General Caching Is Hard: Even with Small Pages

TL;DR

This paper proves that the general caching problem remains strongly NP-hard even with small page sizes of 1, 2, or 3, highlighting the problem's computational difficulty in simplified settings.

Contribution

It provides the first NP-hardness proof for general caching with small pages and offers a concise proof for the problem's strong NP-hardness under these constraints.

Findings

NP-hardness holds for pages of sizes {1, 2, 3}

Proof applies to both fault and bit models

Simplifies understanding of caching complexity with small pages

Abstract

Caching (also known as paging) is a classical problem concerning page replacement policies in two-level memory systems. General caching is the variant with pages of different sizes and fault costs. We give the first NP-hardness result for general caching with small pages: General caching is (strongly) NP-hard even when page sizes are limited to {1, 2, 3}. It holds already in the fault model (each page has unit fault cost) as well as in the bit model (each page has the same fault cost as size). We also give a very short proof of the strong NP-hardness of general caching with page sizes restricted to {1, 2, 3} and arbitrary costs.