外部存储器中最坏情况下的最优树布局
Worst-Case Optimal Tree Layout in External Memory
摘要：
考虑将N个节点的固定拓扑树布置到块大小为B的外部存储器中，以便最小化从根到深度为D的节点的路径所需的最坏情况块存储器传输次数。我们证明了最佳的内存传输次数是$$ \cases{ \displaystyle Θ\left( {D \over \lg (1{+}B)} \right) & when $D = O(\lg N)$, \cr \displaystyle Θ\left( {\lg N \over \lg \left(1{+}{B \lg N \over D}\right)} \right) & when $D = Ω(\lg N)$ and $D = O(B \lg N)$, \cr \displaystyle Θ\left( {D \over B} \right) & when $D = Ω(B \lg N)$. } $$
英文摘要：
Consider laying out a fixed-topology tree of N nodes into external memory with block size B so as to minimize the worst-case number of block memory transfers required to traverse a path from the root to a node of depth D. We prove that the optimal number of memory transfers is $$ \cases{ \displaystyle Θ\left( {D \over \lg (1{+}B)} \right) & when $D = O(\lg N)$, \cr \displaystyle Θ\left( {\lg N \over \lg \left(1{+}{B \lg N \over D}\right)} \right) & when $D = Ω(\lg N)$ and $D = O(B \lg N)$, \cr \displaystyle Θ\left( {D \over B} \right) & when $D = Ω(B \lg N)$. } $$
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