Randomized Paging by Guessing the Future
msra(2009)
摘要
We revisit a classic problem in computer science, the paging problem. In the paging problem, we have a set of n possible pages and a cache of fixed size k, which can store any k of the n pages at a time. At each time step, one of the n pages is requested, and we seek to minimize the number of page faults, which occur if a requested page is not in the cache at the current time. It has been known for nearly 20 years that a randomized paging algorithm, against an oblivious adversary, can achieve a competitive ratio of Hk, the kth harmonic number, and that this is tight. The first such minimax optimal algorithm was by McGeoch and Sleator in 1991, and another was discovered by Achlioptas, Chrobak and Noga in 2000. We present a third such algorithm, GuessTheFuture, which is trivial to state and requires only a simple reduction to OPT, the optimal offline algorithm. The algorithm is simply this: pick a random permutation R of all n possible pages and, at each time step, set your cache to be the cache that OPT would have had at the current time assuming that the future request sequence was R. In other words, the algorithm "guesses" a random future and plays as OPT would according to this guess.
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关键词
competitive ratio,random permutation,harmonic number
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