We address the tradeo between the competitive ratio and the resources used by randomized on-line algorithms for caching. Two algorithms reported in the literature that achieve the optimal ratio H k require a lot of memory and perform extensive computation at each step. On the other hand, a very simple algorithm called RMARK has competitive ratio 2H k -1, within a factor of 2 of the optimum. A natural question that arises here is whether there is a tradeo between simplicity and the competitive ratio. In particular, is it possible to achieve a competitive ratio better than 2H k -1 with a simple algorithm like RMARK?
We ΓΏrst consider marking algorithms that are natural generalizations of RMARK, and we prove that, for any ΒΏ 0, there is no randomized marking algorithm for caching with competitive ratio (2 -)H k . Thus RMARK is essentially optimal among marking algorithms.
Another model of simple caching algorithms is that of trackless algorithms. These are algorithms that do not store any information about items that are not in the cache. It is known that, for k = 2, there is no randomized trackless algorithm for caching with ratio better than 37 24 β 1:5416. The trivial upper bound is 2, achieved even by deterministic algorithms LRU and FIFO. We reduce this gap by giving a trackless randomized algorithm with competitive ratio