Amortized efficiency of list update and paging rules
Communications of the ACM
A model for hierarchical memory
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
An optimal online algorithm for metrical task systems
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Competitive algorithms for server problems
Journal of Algorithms
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Approximation algorithms for NP-hard problems
Competitive algorithms for multilevel caching and relaxed list update
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
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We consider an extension of the two-level paging problem. Besides a fast memory (the cache) and a slow memory, we postulate a third memory, called the "shelf", near the fast memory so that it is more cost-efficient to store or retrieve a page from the shelf than to retrieve a page from the slow memory. Unlike the standard two-level paging problem, the extension is not a special case of the K-server problem as it is not embedded in a space with a symmetric metric. Our goal is to establish an upper bound on the competitive ratio of this "three-level" memory paging problem. We show that unless per page storage costs more than per page retrieval from the shelf, a simple extension of the well-known LRU algorithm has competitive ratio of 2k + l + 1, where k and l are, respectively, the capacities of the cache and the shelf. If, in addition, k ≤ l, then the same algorithm is k + l + 2-competitive.