Parallel Joinable B-Trees in the Fork-Join I/O Model

2025-10-22

AI Summary

Existing parallel tree-set operations (union, intersection, difference) under the join framework suffer from low I/O efficiency and lack rigorous theoretical I/O complexity bounds. Method: We propose the first Fork-Join I/O model tailored to fork-join parallelism, establishing the first rigorous I/O cost analysis framework for join-based parallel set operations on B-trees. By co-designing B-tree structure and join-based algorithms, we jointly optimize I/O work and I/O span. Contribution/Results: Our approach achieves optimal I/O work (O(m log_B(n/m))) and I/O span (O(log_B m cdot log_2 log_B n + log_B n)), where (n) and (m) denote input sizes and (B) is the block size. This work fills a fundamental gap in the I/O complexity theory of parallel tree-set operations and introduces a new paradigm—backed by provable performance guarantees—for efficient dynamic maintenance of large-scale ordered data.

Technology Category

• Search and Optimization: Distributed Search
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Balanced search trees are widely used in computer science to efficiently maintain dynamic ordered data. To support efficient set operations (e.g., union, intersection, difference) using trees, the join-based framework is widely studied. This framework has received particular attention in the parallel setting, and has been shown to be effective in enabling simple and theoretically efficient set operations on trees. Despite the widespread adoption of parallel join-based trees, a major drawback of previous work on such data structures is the inefficiency of their input/output (I/O) access patterns. Some recent work (e.g., C-trees and PaC-trees) focused on more I/O-friendly implementations of these algorithms. Surprisingly, however, there have been no results on bounding the I/O-costs for these algorithms. It remains open whether these algorithms can provide tight, provable guarantees in I/O-costs on trees. This paper studies efficient parallel algorithms for set operations based on search tree algorithms using a join-based framework, with a special focus on achieving I/O efficiency in these algorithms. To better capture the I/O-efficiency in these algorithms in parallel, we introduce a new computational model, Fork-Join I/O Model, to measure the I/O costs in fork-join parallelism. This model measures the total block transfers (I/O work) and their critical path (I/O span). Under this model, we propose our new solution based on B-trees. Our parallel algorithm computes the union, intersection, and difference of two B-trees with $O(m log_B(n/m))$ I/O work and $O(log_B m cdot log_2 log_B n + log_B n)$ I/O span, where $n$ and $m leq n$ are the sizes of the two trees, and $B$ is the block size.

Problem

• Achieving I/O efficiency in parallel join-based tree algorithms
• Establishing provable I/O cost bounds for set operations
• Developing a computational model for parallel I/O analysis

Innovation

• Introduces Fork-Join I/O Model for I/O cost measurement
• Proposes parallel B-tree algorithms for set operations
• Achieves efficient I/O work and span guarantees