多级存储层次结构中的高效树布局
Efficient Tree Layout in a Multilevel Memory Hierarchy
摘要：
我们考虑的问题，布局一棵树与固定的父/子结构的层次存储器。我们的目标是最大限度地减少预期数量的块传输搜索期间沿根到叶路径，叶上的概率分布。这个问题以前被Gil和Itai考虑过，他们在块传输大小B已知的情况下开发了最优但速度较慢的算法。我们提出了更快的，但近似算法相同的问题，最快的算法运行在线性时间，并产生一个解决方案，是在一个附加常数的最佳。此外，我们将展示如何扩展任何近似最优算法的缓存不经意设置中的块传输大小是未知的算法。缓存无关布局的查询性能是在一个恒定的因素的查询性能的最佳已知块大小的布局。计算缓存无关布局只需要在数学上多次调用已知块大小的布局算法;特别是，缓存无关布局可以在O（N lg N）时间内计算，其中N是节点数。最后，我们分析了两个贪婪的策略，并表明，他们有一个性能比之间的Omega（lg B / lg lg B）和O（lg B）的最佳布局相比。
英文摘要：
We consider the problem of laying out a tree with fixed parent/child structure in hierarchical memory. The goal is to minimize the expected number of block transfers performed during a search along a root-to-leaf path, subject to a given probability distribution on the leaves. This problem was previously considered by Gil and Itai, who developed optimal but slow algorithms when the block-transfer size B is known. We present faster but approximate algorithms for the same problem; the fastest such algorithm runs in linear time and produces a solution that is within an additive constant of optimal. In addition, we show how to extend any approximately optimal algorithm to the cache-oblivious setting in which the block-transfer size is unknown to the algorithm. The query performance of the cache-oblivious layout is within a constant factor of the query performance of the optimal known-block-size layout. Computing the cache-oblivious layout requires only logarithmically many calls to the layout algorithm for known block size; in particular, the cache-oblivious layout can be computed in O(N lg N) time, where N is the number of nodes. Finally, we analyze two greedy strategies, and show that they have a performance ratio between Omega(lg B / lg lg B) and O(lg B) when compared to the optimal layout.
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