Competitive Analysis of Randomized Paging Algorithms

The paging problem is defined as follows: we are given a two-level memory system, in which one level is a fast memory, called cache, capable of holding k items, and the second level is an unbounded but slow memory. At each given time step, a request to an item is issued. Given a request to an item p, a miss occurs if p is not present in the fast memory. In response to a miss, we need to choose an item q in the cache and replace it by p. The choice of q needs to be made on-line, without the knowledge of future requests. The objective is to design a replacement strategy with a small number of misses. In this paper we use competitive analysis to study the performance of randomized on-line paging algorithms. Our goal is to show how the concept of work functions, used previously mostly for the analysis of deterministic algorithms, can also be applied, in a systematic fashion, to the randomized case. We present two results: we first show that the competitive ratio of the marking algorithm i..