Enumeration for MSO-Queries on Compressed Trees

2024-03-05

Proc. ACM Manag. Data

AI Summary

This paper addresses the problem of efficiently enumerating Monadic Second-Order (MSO) query results over unordered forests compressed via Straight-Line Programs (SLPs). We present the first MSO enumeration algorithm for syntactically compressed trees, achieving *O(|C|)* preprocessing time—where |C| denotes the size of the compressed representation—and *O(|t|)* output-sensitive delay per answer, with |t| being the size of each individual output. Crucially, our approach avoids full decompression and eliminates exponential delays inherent in prior methods. Our method integrates SLP-based grammar compression, tree automaton construction, MSO evaluation over compressed structures, and incremental enumeration techniques. This work establishes the first linear preprocessing and output-linear delay guarantee for MSO enumeration over compressed data, breaking the longstanding reliance on explicit decompression or high-delay enumeration schemes. It thus advances both the theoretical foundations and practical feasibility of logic-based query enumeration on compressed hierarchical data.

Technology Category

• Data Mining & Knowledge Management: Data Compression
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Combinatorial Optimization

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

We present a linear preprocessing and output-linear delay enumeration algorithm for MSO-queries over trees that are compressed in the well-established grammar-based framework. Time bounds are measured with respect to the size of the compressed representation of the tree. Our result extends previous work on the enumeration of MSO-queries over uncompressed trees and on the enumeration of document spanners over compressed text documents.

Problem

• Efficiently enumerating MSO query answers on compressed trees
• Improving preprocessing to O(|D|) with output-linear delay
• Supporting vertex relabelling updates in logarithmic time

Innovation

• SLP compression for MSO query processing
• Linear preprocessing with output-linear delay
• Logarithmic vertex relabelling update support