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Competitive analysis of randomized paging algorithms
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ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
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ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Frequency capping in online advertising
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
A primal-dual approximation algorithm for min-sum single-machine scheduling problems
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
An O(log k)-competitive algorithm for generalized caching
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A Primal-Dual Randomized Algorithm for Weighted Paging
Journal of the ACM (JACM)
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MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
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We consider online algorithms for the generalized caching problem. Here we are given a cache of size k and pages with arbitrary sizes and fetching costs. Given a request sequence of pages, the goal is to minimize the total cost of fetching the pages into the cache. We give an online algorithm with competitive ratio O(log2k), which is the first algorithm for the problem with competitive ratio sublinear in k. We also give improved O(log k)-competitive algorithms for the special cases of the Bit Model and Fault model. In the Bit Model, the fetching cost is proportional to the size of the page and in the Fault model all fetching costs are uniform. Previously, an O(log2 k)-competitive algorithm due to Irani [14] was known for both of these models. Our algorithms are based on an extension of the primal-dual framework for online algorithms which was developed by Buchbinder and Naor [7]. We first generate an O(log k)-competitive fractional algorithm for the problem. This is done by using a strengthened LP formulation with knapsack-cover constraints, where exponentially many constraints are added upon arrival of a new request. Second, we round online the fractional solution and obtain a randomized online algorithm. Our techniques provide a unified framework for caching algorithms and are substantially simpler than those previously used.