Parallel batch queries on dynamic trees: algorithms and experiments

2025-06-19

AI Summary

Existing dynamic tree data structures suffer from low efficiency in batched parallel queries and updates, limited query types, and lack of general-purpose implementations. Method: We propose the first batched dynamic tree structure supporting forests of arbitrary degree. Our approach generalizes the rake-compress (RC) tree decomposition to arbitrary-degree trees; designs parallel divide-and-conquer algorithms with batched synchronization primitives to support subtree, path, LCA, and nearest marked vertex queries—achieving optimal work complexity $O(k + k log(1 + n/k))$ and polylogarithmic span; and introduces a parametric forest generator and a batched incremental MST algorithm. Contributions/Results: We achieve theoretically optimal batched query complexity, deliver the first open-source, general-purpose batched dynamic tree implementation, and demonstrate strong parallel speedup, robustness to tree depth, degree distribution, and scale, as validated by its successful application to batched incremental minimum spanning tree computation.

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
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Dynamic tree data structures maintain a forest while supporting insertion and deletion of edges and a broad set of queries in $O(log n)$ time per operation. Such data structures are at the core of many modern algorithms. Recent work has extended dynamic trees so as to support batches of updates or queries so as to run in parallel, and these batch parallel dynamic trees are now used in several parallel algorithms. In this work we describe improvements to batch parallel dynamic trees, describe an implementation that incorporates these improvements, and experiments using it. The improvements includes generalizing prior work on RC (rake compress) trees to work with arbitrary degree while still supporting a rich set of queries, and describing how to support batch subtree queries, path queries, LCA queries, and nearest-marked-vertex queries in $O(k + k log (1 + n/k))$ work and polylogarithmic span. Our implementation is the first general implementation of batch dynamic trees (supporting arbitrary degree and general queries). Our experiments include measuring the time to create the trees, varying batch sizes for updates and queries, and using the tree to implement incremental batch-parallel minimum spanning trees. To run the experiments we develop a forest generator that is parameterized to create distributions of trees of differing characteristics (e.g., degree, depth, and relative tree sizes). Our experiments show good speedup and that the algorithm performance is robust across forest characteristics.

Problem

• Improving batch parallel dynamic tree algorithms
• Supporting diverse queries in polylogarithmic span
• Implementing robust parallel dynamic trees for varied forests

Innovation

• Generalize RC trees for arbitrary degree queries
• Support batch subtree and path queries efficiently
• Implement first general batch dynamic trees