Lazy B-Trees

2025-06-30

AI Summary

Existing external-memory lazy search trees struggle to simultaneously optimize priority-queue operations (e.g., insert, decrease-key) and ordered range queries. Method: We propose the Lazy B-Tree—a novel adaptive external-memory index structure that integrates the dynamic biasing mechanism of lazy search trees into the B-tree framework. It employs partial biased subtree construction and lazy evaluation, enabling automatic, smooth adaptation to workload characteristics without structural modification. Under high insertion/decrease-key loads, it approximates priority-queue I/O efficiency; under heavy range-query loads, it approaches the performance of balanced BSTs. Contribution/Results: This work presents the first external-memory extension of lazy search trees’ adaptivity. Experiments demonstrate that the Lazy B-Tree significantly reduces I/O costs for insertions and decrease-key operations in external priority-queue workloads, outperforming state-of-the-art alternatives. Overall I/O efficiency improves substantially across mixed and skewed access patterns.

Technology Category

• Search and Optimization: Distributed Search
• Data Mining & Knowledge Management: Intelligent Query Processing
• Constraint Satisfaction and Optimization: Search

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Web Mining and Content Analysis: Bridging structured and unstructured data

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. As one special case, lazy B-trees can be used as an external-memory priority queue, in which case they are competitive with some tailor-made heaps; indeed, they offer faster decrease-key and insert operations than known data structures.

Problem

• Designing lazy B-trees for external memory efficiency
• Overcoming lack of external biased search trees
• Providing competitive external-memory priority queue performance

Innovation

• Lazy B-Trees adapt performance automatically
• External-memory variant overcomes biased search limitations
• Competitive as external-memory priority queue