文件束缓存的最优在线算法及其在分布式缓存中的推广
Optimal Online Algorithms for File-Bundle Caching and Generalization to Distributed Caching
摘要：
我们考虑一个泛化的标准缓存问题，称为文件束缓存，不同的查询（任务），每个包含$l\ge 1$文件，顺序到达。一个在线算法，不知道查询的顺序提前必须自适应地决定什么文件保持在高速缓存中，以招致最小数量的高速缓存未命中。这里，高速缓存未命中是指查询中的至少一个文件在高速缓存文件中缺失的情况。在$l=1$的特殊情况下，该问题简化为标准高速缓存问题。我们首先分析了经典的最近最少使用（LRU）算法在这种情况下的性能，并表明LRU是一个接近最佳的在线确定性算法的文件束缓存方面的竞争比。然后，我们将我们的结果扩展到一个广义的$(h,k)$分页问题，在这个文件束设置，其中的性能与缓存大小$k$的在线算法相比，一个较小的缓存大小$h<k$的最佳离线基准。在后一种情况下，我们提供了一个随机的$O(l \ln \frac{k}{k-h})$竞争算法，我们的广义$(h,k)$寻呼问题，它可以被看作是一个经典的标记算法的扩展。我们完成了这个结果，提供了一个匹配的竞争比的下限，表明这种修改后的标记算法的性能是在任何随机化的在线算法的两个因素。最后，我们看看分布式版本的文件束缓存问题，其中有$m\ge 1$相同的缓存系统。在这种情况下，我们表明，对于$m=l+1$缓存，有一个确定性的分布式缓存算法，这是$(l^2+l)$竞争和随机分布式缓存算法，这是$O(l\ln(2l+1))$竞争时，$l\ge 2$。
英文摘要：
We consider a generalization of the standard cache problem called file-bundle caching, where different queries (tasks), each containing $l\ge 1$ files, sequentially arrive. An online algorithm that does not know the sequence of queries ahead of time must adaptively decide on what files to keep in the cache to incur the minimum number of cache misses. Here a cache miss refers to the case where at least one file in a query is missing among the cache files. In the special case where $l=1$, this problem reduces to the standard cache problem. We first analyze the performance of the classic least recently used (LRU) algorithm in this setting and show that LRU is a near-optimal online deterministic algorithm for file-bundle caching with regard to competitive ratio. We then extend our results to a generalized $(h,k)$-paging problem in this file-bundle setting, where the performance of the online algorithm with a cache size $k$ is compared to an optimal offline benchmark of a smaller cache size $h<k$. In this latter case, we provide a randomized $O(l \ln \frac{k}{k-h})$-competitive algorithm for our generalized $(h,k)$-paging problem, which can be viewed as an extension of the classic marking algorithm. We complete this result by providing a matching lower bound for the competitive ratio, indicating that the performance of this modified marking algorithm is within a factor of two of any randomized online algorithm. Finally, we look at the distributed version of the file-bundle caching problem where there are $m\ge 1$ identical caches in the system. In this case we show that for $m=l+1$ caches, there is a deterministic distributed caching algorithm which is $(l^2+l)$-competitive and a randomized distributed caching algorithm which is $O(l\ln(2l+1))$-competitive when $l\ge 2$.
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