Towards Lazy B-Trees

TL;DR

The paper addresses the challenge of building adaptive, I/O-efficient dynamic sorted dictionaries in external memory. It extends the adaptive framework of lazy search trees to the external-memory setting by introducing lazy B-trees, a three-layer design, and a weight-based partitioning scheme with doubly-exponential bucket sizes to realize a practical subset of biased-top-layer guarantees. Key contributions include a novel external-memory construction that supports LST-like adaptivity under I/O constraints and the integration of this approach into an I/O-efficient lazy-B-tree framework. This work enables more efficient database indexing and similar workloads by combining adaptive performance with minimized I/O costs in external memory.

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.

Figures (1)

• Figure 1: Schematic view of the original lazy search tree data structure SandlundWild20.