Memory versus randomization in on-line algorithms

On-line algorithms service sequences of requests, one at a time, without knowing future requests. We compare their performance with the performance of algorithms that generate the sequences and service them as well. In many settings, on-line algorithms perform almost as well as optimal off-line algorithms, by using statistics about previous requests in the sequences. Since remembering such information may be expensive, we consider the use of randomization to eliminate memory. In the process, we devise and study performance measures for randomized on-line algorithms. We develop and analyze memoryless randomized on-line algorithms for the cacheing problem and its generalizations.