A Competitive Online Algorithm for the Paging Problem with “Shelf” Memory

Abstract

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.

The research is partially supported by Chung-Ang University Research Grant 96-106.