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.

翻译：在马尔可夫分页模型中，假设页面请求由内存中页面上的马尔可夫链生成，目标是维护一个快速缓存，使其期望缺页次数尽可能少。虽然计算该问题的最优在线算法（$\mathrm{OPT}$）朴素方法所需时间与缓存大小呈指数关系，但最著名的多项式时间近似算法是由Lund、Phillips和Reingold（FOCS 1994）提出的主导分布算法，他们证明该算法相对于$\mathrm{OPT}$是4-竞争的。我们大幅改进了他们的分析，并证明该算法实际上相对于$\mathrm{OPT}$是2-竞争的。我们还给出了该算法的1.5907-竞争性下界——据我们所知，此前尚无此类下界。