Competitive Algorithms for Restricted Caching and Matroid Caching

We study the online restricted caching problem, where each memory item can be placed in only a restricted subset of cache locations. We solve this problem through a more general online caching problem in which the cache is subject to matroid constraints. Our main result is an O( min {d,logr} ·logc)-competitive algorithm for the matroid caching problem, where r and c are the rank and circumference of the matroid, and d is the diameter of an auxiliary graph defined over it. In general, this result guarantees an O(log2 k)-competitiveness for any restricted cache of size k, independently of its structure. In addition, we study the special case of the (n,l)-companion caching problem [8]. For companion caching we prove that our algorithm achieves an optimal competitive factor of O(logn + logl), improving on previous results of [18].

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