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.
- Allan Borodin and Ran El-Yaniv. 1998. Online Computation and Competitive Analysis. Cambridge University Press. Google Scholar
Digital Library
- Thomas M. Cover and Erik Ordentlich. 1996. Universal portfolios with side information. IEEE Trans. Inf. Theory 42, 2, 348--363. Google Scholar
Digital Library
- Ran El-Yaniv. 1998. Competitive solutions for online financial problems. ACM Comput. Surv. 30, 1, 28--69. Google Scholar
Digital Library
- Ran El-Yaniv, Amos Fiat, Richard M. Karp, and G. Turpin. 2001. Optimal search and one-way trading online algorithms. Algorithmica 30, 1, 101--139.Google Scholar
Cross Ref
- Matthias Englert, Berthold Vöcking, and Melanie Winkler. 2009. Economical caching with stochastic prices. In Proceedings of the 5th International Conference on Stochastic Algorithms: Foundations and Applications (SAGA’09). 179--190. Google Scholar
Digital Library
- Sascha Geulen, Berthold Vöcking, and Melanie Winkler. 2010. Regret minimization for online buffering problems using the weighted majority algorithm. In Proceedings of the Conference on Learning Theory (COLT’10). 132--143.Google Scholar
- David P. Helmbold, Robert E. Schapire, Yoram Singer, and Manfred K. Warmuth. 1996. On-line portfolio selection using multiplicative updates. In Proceedings of the 13th International Coriference on Machine Learning (ICML’96). 243--251.Google Scholar
- Erik Ordentlich and Thomas M. Cover. 1996. On-line portfolio selection. In Proceedings of the Conference on Learning Theory (COLT’96). 310--313. Google Scholar
Digital Library
Index Terms
Economical Caching
Recommendations
Tight competitive ratios for parallel disk prefetching and caching
SPAA '08: Proceedings of the twentieth annual symposium on Parallelism in algorithms and architecturesWe consider the natural extension of the well-known single disk caching problem to the parallel disk I/O model (PDM) [17]. The main challenge is to achieve as much parallelism as possible and avoid I/O bottlenecks. We are given a fast memory (cache) of ...
Online algorithms with advice for bin packing and scheduling problems
We consider the setting of online computation with advice and study the bin packing problem and a number of scheduling problems. We show that it is possible, for any of these problems, to arbitrarily approach a competitive ratio of 1 with only a ...
Online Results for Black and White Bin Packing
In online bin packing problems, items of sizes in [0, 1] are to be partitioned into subsets of total size at most 1, called bins. We introduce a new variant where items are of two types, called black and white, and the item types must alternate in each ...






Comments