Towards Lazy B-Trees

TL;DR

This paper introduces lazy B-trees, an external memory data structure that smoothly interpolates between B-trees and binary search trees, optimizing performance based on actual use without adjustments.

Contribution

It extends lazy search trees to external memory, providing a new variant called lazy B-trees that generalize B-tree speedups with a novel construction for external-biased search guarantees.

Findings

Lazy B-trees achieve smooth performance interpolation.

A new external-biased search tree construction is proposed.

The structure improves external memory data management.

Abstract

Lazy search trees (Sandlund & Wild FOCS 2020, Sandlund & Zhang SODA 2022) are sorted dictionaries whose update and query performance smoothly interpolates between that of efficient priority queues and binary search trees - automatically, depending on actual use; no adjustments are necessary to the data structure to realize the cost savings. In this paper, we design lazy B-trees, a variant of lazy search trees suitable for external memory that generalizes the speedup of B-trees over binary search trees wrt. input/output operations to the same smooth interpolation regime. A key technical difficulty to overcome is the lack of a (fully satisfactory) external variant of biased search trees, on which lazy search trees crucially rely. We give a construction for a subset of performance guarantees sufficient to realize external-memory lazy search trees, which we deem of independent interest.