The $B^{\epsilon}$-tree [Brodal and Fagerberg 2003] is a simple I/O-efficient external-memory-model data structure that supports updates orders of magnitude faster than B-tree with a query performance comparable to the B-tree: for any positive constant $\epsilon<1$ insertions and deletions take $O(\frac{1}{B^{1-\epsilon}}\log_{B}N)$ time (rather than $O(\log_BN)$ time for the classic B-tree), queries take $O(\log_BN)$ time and range queries returning $k$ items take $O(\log_BN+\frac{k}{B})$ time. Although the $B^{\epsilon}$-tree has an optimal update/query tradeoff, the runtimes are amortized. Another structure, the write-optimized skip list, introduced by Bender et al. [PODS 2017], has the same performance as the $B^{\epsilon}$-tree but with runtimes that are randomized rather than amortized. In this paper, we present a variant of the $B^{\epsilon}$-tree with deterministic worst-case running times that are identical to the original's amortized running times.

翻译：$B ⁇ epsilon $[Brodal 和 Fagerberg 2003] 是一个简单的 I/ O- O- effective 外部模型数据结构,它支持比 B- Tree 更快的更新数量级,比 B- Tree 的查询性能要快: 任何正数的 $\ epsilon < 1 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\N\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\