External-memory dictionaries with worst-case update cost

TL;DR

This paper introduces a deterministic variant of the $B^{psilon}$-tree, achieving worst-case update times comparable to the original's amortized performance, enhancing reliability for external-memory data structures.

Contribution

The paper presents a new version of the $B^{psilon}$-tree with worst-case guarantees matching the original's amortized bounds, improving its practical applicability.

Findings

Achieves worst-case update times equal to amortized bounds

Maintains query performance comparable to classic B-trees

Provides deterministic guarantees for external-memory dictionaries

Abstract

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.