## Elastic caching

Motivated by applications in cloud computing, we study the classical online caching problem for a cache of variable size, where the algorithm pays a maintenance cost that monotonically increases with cache size. This captures not only the classical setting of a fixed cache size, which corresponds to a maintenance cost of 0 for a cache of size at most k and ∞ otherwise, but also other natural settings in the context of cloud computing such as a concave rental cost on cache size. We call this the elastic caching problem. Our results are: (a) a randomized algorithm with a competitive ratio of O(log n) for maintenance cost that is an arbitrary function of cache size, (b) a deterministic algorithm with a competitive ratio of 2 for concave, or more generally submodular maintenance costs, (c) a deterministic n-competitive algorithm when the cost function is any monotone non-negative set function, and (d) a randomized constant-factor approximation algorithm for the offline version of the problem. Our algorithms are based on a configuration LP formulation of the problem, for which our main technical contribution is to maintain online a feasible fractional solution that can be converted to an integer solution using existing rounding techniques.

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*Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms*(pp. 143–156). https://doi.org/10.1137/1.9781611975482.10

*Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms*, 143–56, 2019. https://doi.org/10.1137/1.9781611975482.10.

*Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms*, 2019, pp. 143–56.

*Scopus*, doi:10.1137/1.9781611975482.10.