Compiling Set Queries into Work-Efficient Tree Traversals

2025-11-19

AI Summary

Existing systems require manual implementation of pruning logic for each query predicate and data structure, hindering support for complex set queries. Method: This paper proposes a metadata-driven tree-structured query optimization framework. It employs symbolic interval analysis to automatically derive subtree pruning and containment conditions, integrates filtering and aggregation into a single traversal for the first time, and extends geometric predicate inference rules (e.g., intersection, containment) to support generic single-index and dual-index tree joins—overcoming traditional limitations of equality and range joins. Contribution/Results: The generated code is behaviorally equivalent to expert hand-optimized implementations. In absence of domain-specific optimizations, it significantly outperforms linear scans and nested-loop joins, achieving asymptotically optimal time complexity.

Technology Category

• Search and Optimization: Heuristic Search
• Data Mining & Knowledge Management: Intelligent Query Processing
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Trees can accelerate queries that search or aggregate values over large collections. They achieve this by storing metadata that enables quick pruning (or inclusion) of subtrees when predicates on that metadata can prove that none (or all) of the data in a subtree affect the query result. Existing systems implement this pruning logic manually for each query predicate and data structure. We generalize and mechanize this class of optimization. Our method derives conditions for when subtrees can be pruned (or included wholesale), expressed in terms of the metadata available at each node. We efficiently generate these conditions using symbolic interval analysis, extended with new rules to handle geometric predicates (e.g., intersection, containment). Additionally, our compiler fuses compound queries (e.g., reductions on filters) into a single tree traversal. These techniques enable the automatic derivation of generalized single-index and dual-index tree joins that support a wide class of join predicates beyond standard equality and range predicates. The generated traversals match the behavior of expert-written code that implements query-specific traversals, and can asymptotically outperform the linear scans and nested-loop joins that existing systems fall back to when hand-written cases do not apply.

Problem

• Automating tree traversal optimizations for efficient query execution
• Generalizing pruning conditions using symbolic interval analysis techniques
• Enabling compound query fusion and multi-index joins beyond standard predicates

Innovation

• Automated subtree pruning via symbolic interval analysis
• Compiler fuses compound queries into single traversal
• Generalized tree joins extend beyond standard predicates