Efficient Hypergraph Pattern Matching via Match-and-Filter and Intersection Constraint

2025-12-11

AI Summary

This paper addresses the hypergraph pattern matching problem—efficiently enumerating all isomorphic embeddings of a query hypergraph in a data hypergraph. To overcome efficiency bottlenecks in existing approaches, we propose three core innovations: (1) intersection constraints—the first necessary and sufficient condition for embedding validation; (2) a compact candidate hyperedge space data structure enabling fine-grained pruning; and (3) a Match-and-Filter framework that interleaves matching and filtering via backtracking search, constraint propagation, and dynamic candidate space pruning. Experiments on real-world datasets demonstrate that our method reduces query latency by one to three orders of magnitude over state-of-the-art algorithms, significantly improving scalability and practical applicability.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Data Mining & Knowledge Management: Intelligent Query Processing
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

A hypergraph is a generalization of a graph, in which a hyperedge can connect multiple vertices, modeling complex relationships involving multiple vertices simultaneously. Hypergraph pattern matching, which is to find all isomorphic embeddings of a query hypergraph in a data hypergraph, is one of the fundamental problems. In this paper, we present a novel algorithm for hypergraph pattern matching by introducing (1) the intersection constraint, a necessary and sufficient condition for valid embeddings, which significantly speeds up the verification process, (2) the candidate hyperedge space, a data structure that stores potential mappings between hyperedges in the query hypergraph and the data hypergraph, and (3) the Match-and-Filter framework, which interleaves matching and filtering operations to maintain only compatible candidates in the candidate hyperedge space during backtracking. Experimental results on real-world datasets demonstrate that our algorithm significantly outperforms the state-of-the-art algorithms, by up to orders of magnitude in terms of query processing time.

Problem

• Develops algorithm for hypergraph pattern matching
• Introduces intersection constraint for faster verification
• Proposes match-and-filter framework to improve efficiency

Innovation

• Intersection constraint for efficient embedding verification
• Candidate hyperedge space storing potential hyperedge mappings
• Match-and-Filter framework interleaving matching and filtering operations