New and Improved Bounds for Markov Paging

Fuente: arXiv
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Autori principali: Pabbaraju, Chirag, Vakilian, Ali
Natura: Preprint
Pubblicazione: 2025
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author Pabbaraju, Chirag
Vakilian, Ali
author_facet Pabbaraju, Chirag
Vakilian, Ali
contents In the Markov paging model, one assumes that page requests are drawn from a Markov chain over the pages in memory, and the goal is to maintain a fast cache that suffers few page faults in expectation. While computing the optimal online algorithm $(\mathrm{OPT})$ for this problem naively takes time exponential in the size of the cache, the best-known polynomial-time approximation algorithm is the dominating distribution algorithm due to Lund, Phillips and Reingold (FOCS 1994), who showed that the algorithm is $4$-competitive against $\mathrm{OPT}$. We substantially improve their analysis and show that the dominating distribution algorithm is in fact $2$-competitive against $\mathrm{OPT}$. We also show a lower bound of $1.5907$-competitiveness for this algorithm -- to the best of our knowledge, no such lower bound was previously known.
format Preprint
id arxiv_https___arxiv_org_abs_2502_05511
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle New and Improved Bounds for Markov Paging
Pabbaraju, Chirag
Vakilian, Ali
Data Structures and Algorithms
In the Markov paging model, one assumes that page requests are drawn from a Markov chain over the pages in memory, and the goal is to maintain a fast cache that suffers few page faults in expectation. While computing the optimal online algorithm $(\mathrm{OPT})$ for this problem naively takes time exponential in the size of the cache, the best-known polynomial-time approximation algorithm is the dominating distribution algorithm due to Lund, Phillips and Reingold (FOCS 1994), who showed that the algorithm is $4$-competitive against $\mathrm{OPT}$. We substantially improve their analysis and show that the dominating distribution algorithm is in fact $2$-competitive against $\mathrm{OPT}$. We also show a lower bound of $1.5907$-competitiveness for this algorithm -- to the best of our knowledge, no such lower bound was previously known.
title New and Improved Bounds for Markov Paging
topic Data Structures and Algorithms
url https://arxiv.org/abs/2502.05511