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.

翻译：精确子图匹配是一种基础图算子，支持众多图分析任务，但由于其NP完全性，计算上仍具有挑战性。近期基于学习的方法通过保持支配性的顶点嵌入加速查询处理，但这些方法存在离线训练成本高、剪枝效果有限以及对复杂索引结构依赖性强的问题，所有这些都阻碍了其在大规模图上的可扩展性。本文提出\textit{\underline{L}earnable Monoton\underline{I}c \underline{V}ertex \underline{E}mbedding}（\textsc{LIVE}），一种可扩展至大规模图的高效精确子图匹配学习框架。\textsc{LIVE}通过设计强制顶点嵌入之间的单调性，使支配正确性成为内在结构属性，并使得嵌入学习能够直接优化顶点层面的剪枝能力。为此，我们引入一个具有可微分替代目标的查询成本模型，以指导高效的离线训练。此外，我们设计了一种轻量级一维\textit{iLabel}索引，该索引保留支配关系并支持高效在线查询处理。在合成数据集和真实数据集上的大量实验表明，\textsc{LIVE}在效率和剪枝效果上显著优于现有最先进方法。