New and Improved Bounds for Markov Paging

TL;DR

This paper improves the theoretical bounds for the Markov paging problem by showing the dominating distribution algorithm is 2-competitive and establishing a new lower bound of 1.5907, enhancing understanding of algorithm performance.

Contribution

The paper provides a tighter analysis of the dominating distribution algorithm, reducing its competitive ratio from 4 to 2, and introduces a new lower bound of 1.5907 for its competitiveness.

Findings

Dominating distribution algorithm is 2-competitive against OPT.

Established a lower bound of 1.5907 on the algorithm's competitiveness.

Enhanced theoretical understanding of Markov paging algorithms.

Abstract

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.