Paging with Per-Replacement Maximum Delay

2026-08-25

AI Summary

研究探讨了在允许延迟替换的情况下，如何改进经典分页算法。提出了一种确定性和随机性算法来处理这种变化，并分析了其竞争力。

Abstract

Classical paging couples every miss to an immediate replacement. We ask what remains of its algorithmic structure when a miss may wait. In our per-replacement maximum-delay model, loading a pending page costs one unit of movement plus the age of its oldest outstanding request and clears the whole page-specific episode. Equivalently, the instantaneous holding rate is the number of pending pages, rather than the number of pending requests. The classical competitive hierarchy survives this change. For cache size $k$, we give a deterministic $(5k+3)$-competitive threshold-LRU algorithm and a randomized $5H_k$-competitive algorithm against an oblivious adversary; classical lower-bound instances give matching $Ω(k)$ and $Ω(H_k)$ orders. The randomized algorithm uses cache-independent temporal windows to create an ordinary-paging sequence fixed before any random choices; a shadow paging algorithm is then projected onto nonproactive physical replacements. The offline picture is less classical. We give an exact $O(nk)$ dynamic program with one hole, an exact configuration dynamic program for a fixed number of holes, and a deterministic nonproactive polynomial-time $5$-approximation without fixing that number. Yet farthest-next-use victim selection can be suboptimal in the physical delayed problem already with three pages.

Problem

• paging
• replacement delay
• competitive analysis

Innovation

• per-replacement maximum-delay model
• threshold-LRU algorithm
• randomized 5H_k-competitive algorithm
• offline O(nk) dynamic program
• configuration dynamic program