A Primal-Dual Randomized Algorithm for Weighted Paging

13 years 10 months ago

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In the weighted paging problem there is a weight (cost) for fetching each page into the cache. We design a randomized O(log k)-competitive online algorithm for the weighted paging problem, where k is the cache size. This is the ﬁrst randomized o(k)-competitive algorithm and its competitiveness matches the known lower bound on the problem. More generally, we design an O(log(k/(k − h + 1)))-competitive online algorithm for the version of the problem where the online algorithm has cache size k and the ofﬂine algorithm has cache size h ≤ k. Weighted paging is a special case (weighted star metric) of the well known k-server problem for which it is a major open question whether randomization can be useful in obtaining subompetitive algorithms. Therefore, abstracting and extending the insights from paging is a key step in the resolution of the k-server problem. Our solution for the weighted paging problem is based on a two-step approach. In the ﬁrst step we obtain an O(log k)-compe...

Nikhil Bansal, Niv Buchbinder, Joseph Naor

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