We present efficient fully persistent B-trees in the I/O model with block size B that support range searches on t reported elements at any accessed version of size n in $O({\log }_{B}n+t/B)$ I/Os and updates at any accessed version in $O({\log }_{B}n+{\log }_{2}B)$ amortized I/Os, using $O(m/B)$ disk blocks after m updates. This improves both the query and update I/O-efficiency of the previous fully persistent B-trees of Lanka and Mays (ACM SIGMOD ICMD 1991).

To achieve the result, we introduce an implementation for ephemeral B-trees that supports searches and updates in $O({\log }_{B}n)$ I/Os, using $O(n/B)$ blocks, where moreover every update makes a worst-case constant number of modifications to the structure. We make these B-trees fully persistent using an I/O-efficient method for full persistence, inspired by the node-splitting method of Driscoll et al. (JCSS 1989). Interesting in its own right, the method is generic enough to be applied to any external memory pointer-based data structure with maximum in-degree $d_{in}$ and out-degree $O\left(B\right)$, where every node occupies a constant number of blocks on disk. For a user-specified parameter $\pi =\mathrm{\Omega }\left(d_{in}\right)$, we achieve $O(\frac{\pi }{B}+{\log }_2\pi )$ I/O-overhead per access to a field of an ephemeral block and amortized $O(\frac{\pi }{B}+{\log }_2\pi +\frac{d_{in}}{\pi }{\log }_{2}B)$ I/O-overhead and $O(1/B)$ block space-overhead per modification to the ephemeral structure.

我们本高效充分持久与块大小的I / O模型B树乙上支持范围搜索吨报道大小的任何访问版本元件Ñ在$Ø（{\mathrm{日志}}_{乙}ñ+Ť/乙）$ I / O和更新的任何版本 $Ø（{\mathrm{日志}}_{乙}ñ+{\mathrm{日志}}_2乙）$ 摊销的I / O，使用 $Ø（米/乙）$m个更新后的磁盘块。这改善了Lanka和Mays先前完全持久的B树的查询和更新I / O效率（ACM SIGMOD ICMD 1991）。

为了获得结果，我们介绍了一个临时B树的实现，该实现支持在中搜索和更新 $Ø（{\mathrm{日志}}_{乙}ñ）$ I / O，使用 $Ø（ñ/乙）$块，此外，每次更新都会对结构进行最坏情况的恒定数量的修改。在Driscoll等人的节点拆分方法的启发下，我们使用I / O有效的方法对这些B树进行完全持久化以实现完全持久。（JCSS 1989）。有趣的是，该方法具有足够的通用性，可以应用于具有最大插入度的任何基于外部存储器指针的数据结构$d_{\mathrm{一世}ñ}$ 和学位 $Ø（乙）$，其中每个节点在磁盘上占据恒定数量的块。对于用户指定的参数$\pi =\mathrm{\Omega }（d_{\mathrm{一世}ñ}）$，我们实现 $Ø（\frac{\pi }{乙}+{\mathrm{日志}}_2\pi ）$ 每次访问临时块并摊销的I / O开销 $Ø（\frac{\pi }{乙}+{\mathrm{日志}}_2\pi +\frac{d_{\mathrm{一世}ñ}}{\pi }{\mathrm{日志}}_2乙）$ I / O开销和 $Ø（\mathrm{1个}/乙）$ 对临时结构的每次修改都会阻止空间开销。