LIVE: Learnable Monotonic Vertex Embedding for Efficient Exact Subgraph Matching (Technical Report)

2026-04-21

AI Summary

Exact subgraph matching is computationally expensive due to its NP-completeness, and existing learning-based approaches suffer from high training costs, weak pruning capability, and reliance on complex indexing structures. To address these limitations, this work proposes LIVE, a novel framework that leverages learnable monotonic vertex embeddings to guarantee correctness of domination relations and directly optimizes vertex-level pruning effectiveness. The core innovations include an embedding mechanism with intrinsic monotonic structure, a differentiable proxy-based query cost model for end-to-end optimization, and a lightweight one-dimensional iLabel index. Experimental results demonstrate that LIVE substantially outperforms state-of-the-art methods on both synthetic and real-world datasets, achieving significant improvements in both efficiency and pruning performance.

Technology Category

• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• 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: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Exact subgraph matching is a fundamental graph operator that supports many graph analytics tasks, yet it remains computationally challenging due to its NP-completeness. Recent learning-based approaches accelerate query processing via dominance-preserving vertex embeddings, but they suffer from expensive offline training, limited pruning effectiveness, and heavy reliance on complex index structures, all of which hinder the scalability to large graphs. In this paper, we propose \textit{\underline{L}earnable Monoton\underline{I}c \underline{V}ertex \underline{E}mbedding} (\textsc{LIVE}), a learning-based framework for efficient exact subgraph matching that scales to large graphs. \textsc{LIVE} enforces monotonicity among vertex embeddings by design, making dominance correctness an inherent structural property and enabling embedding learning to directly optimize vertex-level pruning power. To this end, we introduce a query cost model with a differentiable surrogate objective to guide efficient offline training. Moreover, we design a lightweight one-dimensional \textit{iLabel} index that preserves dominance relationships and supports efficient online query processing. Extensive experiments on both synthetic and real-world datasets demonstrate that \textsc{LIVE} significantly outperforms state-of-the-art methods in efficiency and pruning effectiveness.

Problem

• exact subgraph matching
• vertex embedding
• pruning effectiveness
• scalability
• NP-completeness

Innovation

• monotonic embedding
• subgraph matching
• pruning effectiveness
• learnable index
• dominance-preserving