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More On Randomized On-Line Algorithms For Caching
We address the tradeoff 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 Hk 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 2Hk−1, within a factor of 2 of the optimum. A natural question that arises here is whether there is a tradeoff between simplicity and the competitive ratio. In particular, is it possible to achieve a competitive ratio better than 2Hk−1 with a simple algorithm like RMARK? We first consider marking algorithms that are natural generalizations of RMARK, and we prove that, for any ε>0, there is no randomized marking algorithm for caching with competitive ratio (2−ε)Hk. 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 3724≈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 14(3+13)≈1.6514.