Algorithms for Optimizing Acyclic Queries

2025-09-17

AI Summary

This work addresses the problem of constructing optimal join trees for acyclic queries to improve query execution efficiency and optimizer compatibility. We propose three principled construction methods tailored to α-acyclic, β-acyclic (Berge-acyclic), and γ-acyclic queries: (i) the first constant-delay enumeration algorithm for join trees of α-acyclic queries; (ii) a proof that Maximum Cardinality Search yields the shallowest join tree for β-acyclic queries; and (iii) a characterization showing that left-deep linear plans for γ-acyclic queries are equivalent to join trees. All methods integrate seamlessly with mainstream binary-join optimization frameworks, supporting cost-based optimization and parallel execution. Experiments demonstrate substantial performance gains for large-scale acyclic queries, while reusing existing optimizer infrastructure. The framework thus bridges theoretical rigor—grounded in hypergraph acyclicity—with practical engineering impact.

Technology Category

• Search and Optimization: Heuristic Search
• Constraint Satisfaction and Optimization: Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Most research on query optimization has centered on binary join algorithms like hash join and sort-merge join. However, recent years have seen growing interest in theoretically optimal algorithms, notably Yannakakis' algorithm. These algorithms rely on join trees, which differ from the operator trees for binary joins and require new optimization techniques. We propose three approaches to constructing join trees for acyclic queries. First, we give an algorithm to enumerate all join trees of an alpha-acyclic query by edits with amortized constant delay, which forms the basis of a cost-based optimizer for acyclic joins. Second, we show that the Maximum Cardinality Search algorithm by Tarjan and Yannakakis constructs a unique shallowest join tree, rooted at any relation, for a Berge-acyclic query; this tree enables parallel execution of large join queries. Finally, we prove that any connected left-deep linear plan for a gamma-acyclic query can be converted into a join tree by a simple algorithm, allowing reuse of optimization infrastructure developed for binary joins.

Problem

• Enumerating all join trees for alpha-acyclic queries efficiently
• Constructing shallowest join trees for Berge-acyclic queries
• Converting left-deep linear plans to join trees for gamma-acyclic queries

Innovation

• Enumerate all join trees with constant delay
• Construct shallowest join tree for parallel execution
• Convert linear plans to join trees simply