External-memory dictionaries with worst-case update cost

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 $O(\logBN)$ time for the classic B-tree), queries take $O(\logBN)$ 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.