论文标题

缓存的空间位置和粒度变化

Spatial Locality and Granularity Change in Caching

论文作者

Beckmann, Nathan, Gibbons, Phillip B, McGuffey, Charles

论文摘要

缓存利用时间和空间局部性,以允许少量内存提供对存储在大而缓慢内存中的数据的快速访问。当地的时间方面对研究和理解是非常充分的,但是空间方面的程度要少得多。我们试图通过定义和研究粒度变化的缓存问题来增加对空间位置的了解。此问题通过将数据项分组到块中来修改传统的缓存设置,以便缓存可以选择块的任何子集以与将任何单独项目加载到块中相同的成本加载。 我们表明,建模这种空间位置会显着改变缓存问题。这首先要证明颗粒状变化缓存在离线设置中是NP填充,即使所有项目具有单位尺寸,并且所有块都具有单位负载成本。在在线环境中,我们显示了确定性政策的竞争比率的下限,这比传统的缓存明显差。此外,我们提出了一种确定性替代政策,称为项目块分层分区,并表明它获得了接近该下限的竞争比率。此外,我们的界限揭示了一个新问题,这是在粒度变化的缓存问题中引起的,即离线缓存大小的选择会影响不同在线算法相对于彼此的竞争力。为了解决这个问题,我们将先前的(时间)局部性模型扩展到空间位置,并提供一般的下限,除了用于项目块上层分区的上限外。

Caches exploit temporal and spatial locality to allow a small memory to provide fast access to data stored in large, slow memory. The temporal aspect of locality is extremely well studied and understood, but the spatial aspect much less so. We seek to gain an increased understanding of spatial locality by defining and studying the Granularity-Change Caching Problem. This problem modifies the traditional caching setup by grouping data items into blocks, such that a cache can choose any subset of a block to load for the same cost as loading any individual item in the block. We show that modeling such spatial locality significantly changes the caching problem. This begins with a proof that Granularity-Change Caching is NP-Complete in the offline setting, even when all items have unit size and all blocks have unit load cost. In the online setting, we show a lower bound for competitive ratios of deterministic policies that is significantly worse than traditional caching. Moreover, we present a deterministic replacement policy called Item-Block Layered Partitioning and show that it obtains a competitive ratio close to that lower bound. Moreover, our bounds reveal a new issue arising in the Granularity-Change Caching Problem where the choice of offline cache size affects the competitiveness of different online algorithms relative to one another. To deal with this issue, we extend a prior (temporal) locality model to account for spatial locality, and provide a general lower bound in addition to an upper bound for Item-Block Layered Partitioning.

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