We revisitself-adjustingexternal memory tree data structures, which combine the optimal (and practical) worst-case I/O performances of B-trees, while adapting to the online distribution of queries. Our approach is analogous to undergoing efforts in the BST model, where Tango Trees (Demaine et al., SIAM J. Comput. 37(1), 240–251, 2007) were shown to be \(O(\log \log N)\)-competitive with the runtime of the best offline binary search tree on every sequence of searches. Here we formalize the B-Tree model as a natural generalization of the BST model. We prove lower bounds for the B-Tree model, and introduce a B-Tree model data structure, the Belga B-tree, that executes any sequence of searches within a \(O(\log \log N)\) factor of the best offline B-tree model algorithm, provided \(B=\log ^{O(1)}N\). We also show how to transform any static BST into a static B-tree which is faster by a \({\varTheta }(\log B)\) factor; the transformation is randomized and we show that randomization is necessary to obtain any significant speedup.

我们重新审视自我调整的外部内存树数据结构，该结构结合了B树的最佳（和实际）最坏情况下的I / O性能，同时适应了查询的在线分发。我们的方法是类似于在BST模型，其中正在进行努力探戈树（Demaine等人，SIAM J. COMPUT。37（1），240-251，2007）被证明是\（O（\ LOG \日志N ）\） -与每个搜索序列上最佳离线二进制搜索树的运行时间竞争。在这里，我们将B-Tree模型形式化为BST模型的自然概括。我们证明B树模型的下界，并引入B树模型数据结构Belga B树，该数据结构执行\（O（\ log \ log N）\）内的任何搜索序列最好的离线B树模型算法的系数（\（B = \ log ^ {O（1）} N \）。我们还将展示如何将任何静态BST转换为静态B树，该树可以通过\（{\ varTheta}（\ log B）\）因子更快地转换；转换是随机的，我们证明随机化对于获得明显的加速是必要的。