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Economical Caching

Published:01 July 2013Publication History
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Abstract

We study the management of buffers and storages in environments with unpredictably varying prices in a competitive analysis. In the economical caching problem, there is a storage with a certain capacity. For each time step, an online algorithm is given a price from the interval [1, α], a consumption, and possibly a buying limit. The online algorithm has to decide the amount to purchase from some commodity, knowing the parameter α but without knowing how the price evolves in the future. The algorithm can purchase at most the buying limit. If it purchases more than the current consumption, then the excess is stored in the storage; otherwise, the gap between consumption and purchase must be taken from the storage. The goal is to minimize the total cost. Interesting motivating applications are, for example, stream caching on mobile devices with different classes of service, battery management in micro hybrid cars, and the efficient purchase of resources.

First we consider the simple but natural class of algorithms that can informally be described as memoryless. We show that these algorithms cannot achieve a competitive ratio below √α. Then we present a more sophisticated deterministic algorithm achieving a competitive ratio of where W denotes the Lambert W function. We prove that this algorithm is optimal and that not even randomized online algorithms can achieve a better competitive ratio. On the other hand, we show how to achieve a constant competitive ratio if the storage capacity of the online algorithm exceeds the storage capacity of an optimal offline algorithm by a factor of log α.

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  1. Economical Caching

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    • Published in

      cover image ACM Transactions on Computation Theory
      ACM Transactions on Computation Theory  Volume 5, Issue 2
      July 2013
      104 pages
      ISSN:1942-3454
      EISSN:1942-3462
      DOI:10.1145/2493246
      Issue’s Table of Contents

      Copyright © 2013 ACM

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 1 July 2013
      • Accepted: 1 April 2013
      • Revised: 1 March 2013
      • Received: 1 October 2012
      Published in toct Volume 5, Issue 2

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