Online Paging and Caching

Abstract

A file-caching problem instance specifies a cache size k (a positive integer) and a sequence of requests to files, each with a size (a positive integer) and a retrieval cost (a nonnegative number). The goal is to maintain the cache to satisfy the requests while minimizing the retrieval cost. Specifically, for each request, if the file is not in the cache, one must retrieve it into the cache (paying the retrieval cost) and remove other files to bring the total size of files in the cache to k or less. Weighted caching or weighted paging is the special case when each file size is 1. Paging is the special case when each file size and each retrieval cost is 1 (then the retrieval cost is the number of cache misses, and the fault rate is the average retrieval cost per request). An algorithm is online if its response to each request is independent of later requests. In practice this is generally necessary. Standard worst-case analysis is not meaningful for online algorithms – any algorithm will have some input sequence that forces a retrieval for every request. Yet worst-case analysis can be done meaningfully as follows. An algorithm is c.h; k/-competitive if on any sequence the total (expected) retrieval cost incurred by the algorithm using a cache of size k is at most c.h; k/ times the minimum cost to handle with a cache of size h (plus a constant independent of ). Then the algorithm has competitive ratio c.h; k/. The study of competitive ratios is called competitive analysis. (In the larger context of approximation algorithms for combinatorial optimization, this ratio is commonly called the approximation ratio.)