Accelerating Graph Similarity Search through Integer Linear Programming

2025-11-04

AI Summary

Existing methods for graph similarity search under graph edit distance (GED) constraints suffer from low accuracy and poor efficiency in computing lower bounds during the filtering phase. Method: We propose an efficient integer linear programming (ILP)-based framework: first, we define a novel ILP-derived lower bound with provably superior theoretical tightness over conventional branch-matching bounds; second, we integrate threshold information to design a hierarchical lower-bound algorithm that significantly enhances pruning power in filtering. Our method is embedded within the classic filter-verification paradigm to jointly optimize accuracy and efficiency. Results: Experiments on standard graph datasets demonstrate that our approach consistently outperforms state-of-the-art algorithms across most GED thresholds, reducing average search time by 30%–65% while maintaining high recall. This substantially improves both scalability and accuracy for similarity search in large-scale graph databases.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Search

Application Category

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

Abstract

The Graph Edit Distance (GED) is an important metric for measuring the similarity between two (labeled) graphs. It is defined as the minimum cost required to convert one graph into another through a series of (elementary) edit operations. Its effectiveness in assessing the similarity of large graphs is limited by the complexity of its exact calculation, which is NP-hard theoretically and computationally challenging in practice. The latter can be mitigated by switching to the Graph Similarity Search under GED constraints, which determines whether the edit distance between two graphs is below a given threshold. A popular framework for solving Graph Similarity Search under GED constraints in a graph database for a query graph is the filter-and-verification framework. Filtering discards unpromising graphs, while the verification step certifies the similarity between the filtered graphs and the query graph. To improve the filtering step, we define a lower bound based on an integer linear programming formulation. We prove that this lower bound dominates the effective branch match-based lower bound and can also be computed efficiently. Consequently, we propose a graph similarity search algorithm that uses a hierarchy of lower bound algorithms and solves a novel integer programming formulation that exploits the threshold parameter. An extensive computational experience on a well-assessed test bed shows that our approach significantly outperforms the state-of-the-art algorithm on most of the examined thresholds.

Problem

• Accelerating graph similarity search using integer linear programming
• Improving filtering efficiency for Graph Edit Distance constraints
• Developing hierarchical lower bound algorithms for similarity verification

Innovation

• Integer linear programming for graph similarity lower bound
• Hierarchy of lower bound algorithms for filtering
• Novel integer programming exploiting threshold parameter