The paging problem is that of deciding which pages to keep in a memory of k pages in order to minimize the number of page faults. We develop the marking algorithm, a randomized on-line algorithm for the paging problem. We prove that its expected cost on any sequence of requests is within a factor of 2H k of optimum. (Where H k is the kth harmonic number, which is roughly ln k.) The best such factor that can be achieved is H k . This is in contrast to deterministic algorithms, which cannot be guaranteed to be within a factor smaller than k of optimum. An alternative to comparing an on-line algorithm with the optimum offline algorithm is the idea of comparing it to several other on-line algorithms. We have obtained results along these lines for the paging problem. Given a set of on-line algorithms and a set of appropriate constants, we describe a way of constructing another on-line algorithm whose performance is within the appropriate constant factor of each algorithm in the set.
Fiat et al. REF extend the study to the randomized setting and design a randomized 2H kcompetitive algorithm, where H k is the k-th Harmonic number.
Competitive Paging Algorithms
Journal of Algorithms 12:685-699 (1991)
Computer Science