### A Primal-Dual Randomized Algorithm for Weighted PagingA Primal-Dual Randomized Algorithm for Weighted Paging

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 Author Bansal, Nikhil ♦ Buchbinder, Niv ♦ Naor, Joseph Seffi Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2012 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Weighted paging ♦ Online algorithms ♦ Primal-dual ♦ Randomization Abstract We study the weighted version of the classic online paging problem where there is a weight (cost) for fetching each page into the cache. We design a randomized $\textit{O}(log$ $\textit{k})-competitive$ online algorithm for this problem, where $\textit{k}$ is the cache size. This is the first randomized $\textit{o}(\textit{k})-competitive$ algorithm and its competitive ratio matches the known lower bound for the problem, up to constant factors. More generally, we design an $\textit{O}(log(\textit{k}/(\textit{k}$ ™ $\textit{h}$ + 1)))-competitive online algorithm for the version of the problem where the online algorithm has cache size $\textit{k}$ and it is compared to an optimal offline solution with cache size $\textit{h}$ ≤ $\textit{k}.$ Our solution is based on a two-step approach. We first obtain an $\textit{O}(log$ $\textit{k})-competitive$ fractional algorithm based on an online primal-dual approach. Next, we obtain a randomized algorithm by rounding in an online manner the fractional solution to a probability distribution on the possible cache states. We also give an online primal-dual randomized $\textit{O}(log$ $\textit{N})-competitive$ algorithm for the Metrical Task System problem (MTS) on a weighted star metric on $\textit{N}$ leaves. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2012-08-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 59 Issue Number 4 Page Count 24 Starting Page 1 Ending Page 24

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Source: ACM Digital Library