arxiv: 2604.19116 · v1 · submitted 2026-04-21 · 💻 cs.DB

Recognition: unknown

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

Jianxin Li, Li Sun, Mengyi Yan, Philip S. Yu, Ruijie Wang, Weilong Ren, Yang Liu, Yutong Ye

Pith reviewed 2026-05-10 01:49 UTC · model grok-4.3

classification 💻 cs.DB

keywords exact subgraph matchingvertex embeddingsmonotonicitypruninggraph query processingdominance preservationlearnable index

0 comments

The pith

Monotonic vertex embeddings make dominance relations correct by design for pruning in exact subgraph matching.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces LIVE to tackle the NP-hard problem of exact subgraph matching on large graphs. It enforces monotonicity directly into the vertex embedding process so that if one embedding dominates another, the dominance for safe pruning holds automatically. This lets the learning process focus on maximizing how many vertices can be eliminated early rather than relying on post-hoc checks or complex structures. A query cost model supplies a differentiable surrogate loss for offline training, while a lightweight one-dimensional iLabel index maintains the dominance order for fast online use. The result is a framework intended to deliver stronger pruning and better scalability than prior learning-based approaches.

Core claim

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. It introduces a query cost model with a differentiable surrogate objective to guide efficient offline training and designs a lightweight one-dimensional iLabel index that preserves dominance relationships and supports efficient online query processing.

What carries the argument

Learnable monotonic vertex embeddings: vectors assigned to graph vertices such that dominance in embedding space directly corresponds to dominance in matching potential, allowing training to target pruning power.

If this is right

Embedding learning directly targets vertex-level pruning power instead of indirect proxies.
A lightweight one-dimensional index suffices to support online queries while preserving dominance.
The approach reduces reliance on expensive offline training and heavy index structures compared with prior methods.
Experiments indicate improved efficiency and pruning on both synthetic and real-world graph datasets.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The monotonic design could extend to other dominance-based graph tasks such as motif enumeration or frequent subgraph mining.
If the surrogate loss generalizes, similar differentiable objectives might accelerate other NP-hard graph operators.
Lower index complexity may simplify integration into existing graph database systems.

Load-bearing premise

The differentiable surrogate objective accurately reflects real-world query costs and pruning effectiveness, and the monotonicity constraint does not prevent embeddings from distinguishing matchable vertices.

What would settle it

On a large graph dataset, if embeddings trained under the monotonicity constraint produce lower vertex pruning rates or higher overall query times than embeddings trained without the constraint, the central claim would be falsified.

Figures

Figures reproduced from arXiv: 2604.19116 by Jianxin Li, Li Sun, Mengyi Yan, Philip S. Yu, Ruijie Wang, Weilong Ren, Yang Liu, Yutong Ye.

**Figure 3.** Figure 3: Illustration of our monotonic vertex embedding [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: An illustration of the monotonicity of our vertex embedding. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 6.** Figure 6: An example of optimized VLE/VSE vector distributions. [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

**Figure 8.** Figure 8: An illustration of our iLabel index design [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗

**Figure 10.** Figure 10: LIVE efficiency w.r.t different parameters 𝒅, 𝜶/𝜷, and 𝒕. (a) real-world graphs (b) synthetic graphs [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗

**Figure 12.** Figure 12: LIVE efficiency on synthetic/real-world graphs. examined during index traversal; and (ii) an effective 𝛼/𝛽 can be achieved with a relatively small value (e.g., 105 ). Overall, LIVE maintains low query latency across a wide range of 𝛼/𝛽 values (ranging from 0.06𝑚𝑠 to 1.16𝑚𝑠). Impact of Synopsis Hop Parameter 𝒕 [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗

**Figure 13.** Figure 13: LIVE efficiency evaluation on synthetic graphs. To further evaluate the efficiency of LIVE, we varied key parameters (e.g., |Σ|, 𝑎𝑣𝑔_𝑑𝑒𝑔(𝑞), |𝑉 (𝑞)|, 𝑎𝑣𝑔_𝑑𝑒𝑔(𝐺), and |𝑉 (𝐺)|) on synthetic graphs in subsequent tests. To better illustrate performance trends, baseline results are omitted below. Efficiency of LIVE w.r.t. # of Distinct Vertex Labels, |𝚺|. Figure 13(a) shows the query time of LIVE as the num… view at source ↗

**Figure 14.** Figure 14: The LIVE offline pre-computation cost. This efficiency stems from the one-dimensional iLabel index design combined with effective pruning strategies, which tightly bound candidate exploration even as graph size grows. This indicates that LIVE scales well for exact subgraph matching on large-scale graphs. 6.5 Offline Pre-Computation Performance In this subsection, we evaluated the offline pre-computation c… view at source ↗

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

LIVE bakes monotonicity into the embeddings so dominance pruning is guaranteed by structure, then trains with a differentiable surrogate and a minimal 1D index, but the surrogate's link to real query costs remains the unproven part.

read the letter

LIVE's central idea is to enforce monotonicity among vertex embeddings from the start. That makes the dominance relation for safe pruning a built-in property instead of something the model might get wrong. The authors then train the embeddings with a differentiable surrogate that directly targets pruning power, and they pair it with a lightweight one-dimensional iLabel index that preserves the ordering for fast online checks. This combination is presented as fixing the heavy training and complex indexes in earlier learning-based subgraph matchers while scaling to larger graphs. The structural guarantee on correctness is the cleanest part of the design; it removes a source of error that prior work had to handle separately. The surrogate lets them optimize without running full queries in every training step, and the index stays simple, which matters for practical deployment on big graphs. Those choices look like genuine engineering progress on the problem. The main weakness is exactly the one the stress-test note flags. The surrogate is a proxy for candidate-set size or join cost, but nothing in the abstract shows that it actually tracks measured query latency once the monotonic ordering and iLabel index are applied. If the correlation is weak, the learned embeddings could prune poorly in practice even though they remain safe. The abstract claims outperformance on synthetic and real datasets, yet gives no numbers, no ablations on the monotonicity constraint, and no direct comparison of surrogate values versus observed runtimes. Without those, it is hard to know whether the reported gains come from the new components or from other implementation details. This work is aimed at people who build graph query engines or study learning for NP-hard graph operators. A reader who already follows dominance-based pruning or index design for subgraph matching will see the most value. The paper has a clear technical contribution and enough formal grounding to deserve a serious referee, though any review should press hard on the surrogate validation and the experimental controls.

Referee Report

3 major / 1 minor

Summary. The paper proposes LIVE, a framework for exact subgraph matching on large graphs that uses learnable monotonic vertex embeddings. Monotonicity is enforced by design to make dominance correctness a structural property, allowing the embedding model to directly optimize vertex-level pruning power via a query cost model with a differentiable surrogate objective. A lightweight one-dimensional iLabel index is introduced to preserve dominance relationships for efficient online processing. The authors claim that LIVE scales better than prior learning-based methods and significantly outperforms state-of-the-art approaches in efficiency and pruning effectiveness, supported by experiments on synthetic and real-world datasets.

Significance. If the central claims hold, the structural enforcement of monotonicity is a notable strength because it decouples correctness guarantees from the learned parameters, potentially simplifying deployment and reducing the need for complex post-processing or index structures. The lightweight iLabel index and direct optimization of pruning via the surrogate could improve scalability for subgraph matching in database systems. Credit is due for making dominance an inherent property rather than a learned constraint.

major comments (3)

[Query cost model and surrogate objective] The query cost model and differentiable surrogate objective (introduced to guide offline training) form a load-bearing component of the central claim. The surrogate is constructed to optimize the same pruning power that the method claims to improve, raising a circularity risk; without an explicit correlation analysis between surrogate values and measured online costs (e.g., candidate-set sizes or join latency under the iLabel index), it is unclear whether optimizing the surrogate translates to actual query-time gains.
[Experiments] The abstract asserts that extensive experiments on synthetic and real-world datasets demonstrate outperformance in efficiency and pruning effectiveness, yet no quantitative results, error bars, dataset statistics, baseline details, or ablation studies (e.g., on the impact of the monotonicity constraint) are referenced. This absence prevents verification that the data and methods support the efficiency and scalability claims.
[Monotonicity enforcement] While monotonicity guarantees dominance correctness by construction, the paper must address whether this constraint limits the embeddings' ability to distinguish matchable vertices. An analysis showing that the monotonicity does not unduly reduce expressiveness (or an ablation comparing monotonic vs. unconstrained embeddings) is needed to substantiate that the design choice does not trade off pruning power for safety.

minor comments (1)

[Abstract] The abstract contains LaTeX formatting artifacts (e.g., underlined letters in the acronym expansion) that should be cleaned for readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments and the recommendation for major revision. We appreciate the focus on validating the surrogate objective, strengthening the experimental presentation, and examining potential trade-offs in the monotonicity design. We address each major comment below and will incorporate the suggested additions and clarifications in the revised manuscript.

read point-by-point responses

Referee: [Query cost model and surrogate objective] The query cost model and differentiable surrogate objective (introduced to guide offline training) form a load-bearing component of the central claim. The surrogate is constructed to optimize the same pruning power that the method claims to improve, raising a circularity risk; without an explicit correlation analysis between surrogate values and measured online costs (e.g., candidate-set sizes or join latency under the iLabel index), it is unclear whether optimizing the surrogate translates to actual query-time gains.

Authors: The surrogate is analytically derived from the query cost model to directly target the pruning power measured at runtime. While end-to-end experiments already show query-time improvements, we agree an explicit link is valuable. In the revision we will add a dedicated analysis subsection with correlation plots, Pearson coefficients, and statistics relating surrogate scores to online metrics (candidate-set sizes and iLabel join latencies) across datasets to confirm the surrogate's predictive value. revision: yes
Referee: [Experiments] The abstract asserts that extensive experiments on synthetic and real-world datasets demonstrate outperformance in efficiency and pruning effectiveness, yet no quantitative results, error bars, dataset statistics, baseline details, or ablation studies (e.g., on the impact of the monotonicity constraint) are referenced. This absence prevents verification that the data and methods support the efficiency and scalability claims.

Authors: The abstract follows the conventional high-level summary style; the full manuscript (Section 5) already reports quantitative results, dataset statistics, baseline details, and performance tables. To address the request for greater transparency, we will revise the Experiments section to include error bars on all plots, expanded dataset statistics, and a new ablation study isolating the monotonicity constraint's effect on pruning power and scalability. revision: yes
Referee: [Monotonicity enforcement] While monotonicity guarantees dominance correctness by construction, the paper must address whether this constraint limits the embeddings' ability to distinguish matchable vertices. An analysis showing that the monotonicity does not unduly reduce expressiveness (or an ablation comparing monotonic vs. unconstrained embeddings) is needed to substantiate that the design choice does not trade off pruning power for safety.

Authors: Monotonicity is imposed by design precisely to make dominance a structural guarantee independent of parameter values. To demonstrate that this does not unduly restrict discriminative power, we will add both an embedding-space analysis and an ablation comparing the monotonic model against an unconstrained variant (trained with a soft penalty) with respect to pruning effectiveness, embedding quality metrics, and end-to-end query performance. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected; derivation is self-contained

full rationale

The paper's claimed chain rests on two explicit design choices: (1) monotonicity enforced among embeddings by construction, which structurally guarantees dominance correctness without deriving it from data or prior results, and (2) a differentiable surrogate objective introduced to guide training toward vertex-level pruning power. Neither reduces to its own inputs by construction; the monotonicity property is an architectural constraint, and the surrogate is a training mechanism whose effectiveness is evaluated via independent experiments on synthetic and real-world datasets measuring actual query efficiency and pruning. No equations are shown to equate a fitted parameter directly to a claimed prediction, no self-citations are load-bearing for the central premise, and no uniqueness theorems or ansatzes are imported from prior author work. The derivation therefore remains independent of the inputs it optimizes.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on learned embedding parameters and the assumption that monotonicity preserves pruning correctness; these are not independently verified beyond the abstract's description.

free parameters (1)

Vertex embedding model parameters
Embeddings are produced by a learnable model whose weights are fitted during offline training guided by the surrogate objective.

axioms (1)

domain assumption Enforcing monotonicity among vertex embeddings preserves the correctness of dominance-based pruning decisions.
This assumption allows the paper to treat dominance correctness as an inherent structural property rather than something that must be separately enforced or verified.

invented entities (1)

iLabel index no independent evidence
purpose: Lightweight one-dimensional index that preserves dominance relationships for efficient online query processing.
New index structure introduced to support the embedding-based pruning without heavy storage overhead.

pith-pipeline@v0.9.0 · 5530 in / 1409 out tokens · 64029 ms · 2026-05-10T01:49:29.506612+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

71 extracted references · 2 canonical work pages

[1]

Christopher R Aberger, Andrew Lamb, Susan Tu, Andres Nötzli, Kunle Olukotun, and Christopher Ré. 2017. Emptyheaded: A relational engine for graph processing. ACM Transactions on Database Systems42, 4 (2017), 1–44

2017
[2]

Ahmed Al-Baghdadi and Xiang Lian. 2020. Topic-based community search over spatial-social networks. InProceedings of the International Conference on Very Large Data Bases (PVLDB). 2104–2117

2020
[3]

Uri Alon. 2007. Network motifs: theory and experimental approaches.Nature Reviews Genetics8, 6 (2007), 450–461

2007
[4]

Khaled Ammar, Frank McSherry, Semih Salihoglu, and Manas Joglekar. 2018. Distributed Evaluation of Subgraph Queries Using Worst-case Optimal Low- Memory Dataflows. InProceedings of the International Conference on Very Large Data Bases (PVLDB). 691–704

2018
[5]

Blair Archibald, Fraser Dunlop, Ruth Hoffmann, Ciaran McCreesh, Patrick Prosser, and James Trimble. 2019. Sequential and parallel solution-biased search for subgraph algorithms. InProceedings of the Integration of Constraint Program- ming, Artificial Intelligence, and Operations Research (CPAIOR). 20–38

2019
[6]

László Babai. 2018. Group, graphs, algorithms: the graph isomorphism problem. InProceedings of the International Congress of Mathematicians: Rio de Janeiro

2018
[7]

World Scientific, 3319–3336
[8]

Yunsheng Bai, Hao Ding, Song Bian, Ting Chen, Yizhou Sun, and Wei Wang
[9]

InProceedings of the International Conference on Web Search and Data Mining (WSDM)

Simgnn: A neural network approach to fast graph similarity computation. InProceedings of the International Conference on Web Search and Data Mining (WSDM). 384–392
[10]

Bibek Bhattarai, Hang Liu, and H Howie Huang. 2019. Ceci: Compact embedding cluster index for scalable subgraph matching. InProceedings of the International Conference on Management of Data (SIGMOD). 1447–1462

2019
[11]

Fei Bi, Lijun Chang, Xuemin Lin, Lu Qin, and Wenjie Zhang. 2016. Efficient subgraph matching by postponing cartesian products. InProceedings of the International Conference on Management of Data (SIGMOD). 1199–1214

2016
[12]

Vincenzo Bonnici, Rosalba Giugno, Alfredo Pulvirenti, Dennis Shasha, and Al- fredo Ferro. 2013. A subgraph isomorphism algorithm and its application to biochemical data.BMC Bioinformatics14, 7 (2013), 1–13

2013
[13]

Stephan Borzsony, Donald Kossmann, and Konrad Stocker. 2001. The skyline operator. InProceedings of the International Conference on Data Engineering (ICDE). 421–430

2001
[14]

Vincenzo Carletti, Pasquale Foggia, Alessia Saggese, and Mario Vento. 2017. Challenging the time complexity of exact subgraph isomorphism for huge and dense graphs with VF3.IEEE Transactions on Pattern Analysis and Machine Intelligence40, 4 (2017), 804–818

2017
[15]

Vincenzo Carletti, Pasquale Foggia, and Mario Vento. 2015. VF2 Plus: An im- proved version of VF2 for biological graphs. InInternational Workshop on Graph- Based Representations in Pattern Recognition (GbRPR). 168–177

2015
[16]

Luigi P Cordella, Pasquale Foggia, Carlo Sansone, and Mario Vento. 2004. A (sub) graph isomorphism algorithm for matching large graphs.IEEE Transactions on Pattern Analysis and Machine Intelligence26, 10 (2004), 1367–1372

2004
[17]

Alin Deutsch, Nadime Francis, Alastair Green, Keith Hare, Bei Li, Leonid Libkin, Tobias Lindaaker, Victor Marsault, Wim Martens, Jan Michels, et al. 2022. Graph pattern matching in GQL and SQL/PGQ. InProceedings of the International Conference on Management of Data (SIGMOD). 2246–2258

2022
[18]

Boxin Du, Si Zhang, Nan Cao, and Hanghang Tong. 2017. First: Fast interactive attributed subgraph matching. InProceedings of the International Conference on Knowledge Discovery and Data Mining (SIGKDD). 1447–1456

2017
[19]

Sourav Dutta, Pratik Nayek, and Arnab Bhattacharya. 2017. Neighbor-aware search for approximate labeled graph matching using the chi-square statistics. InProceedings of the Web Conference (WWW). 1281–1290

2017
[20]

Garey and David S

Michael R. Garey and David S. Johnson. 1983. Computers and intractability: A guide to the theory of NP-completeness.The Journal of Symbolic Logic48, 2 (1983), 498–500

1983
[21]

Martin Grohe and Pascal Schweitzer. 2020. The graph isomorphism problem. Commun. ACM63, 11 (2020), 128–134

2020
[22]

Qiuyu Guo, Jianye Yang, Wenjie Zhang, Hanchen Wang, Ying Zhang, and Xuemin Lin. 2025. Efficient and Accurate Subgraph Counting: A Bottom-up Flow-learning Based Approach. InProceedings of the International Conference on Very Large Data Bases (PVLDB). 2695–2708

2025
[23]

Aric Hagberg and Drew Conway. 2020. Networkx: Network analysis with python. URL: https://networkx. github. io(2020)

2020
[24]

Myoungji Han, Hyunjoon Kim, Geonmo Gu, Kunsoo Park, and Wook-Shin Han
[25]

InProceedings of the International Conference on Management of Data (SIGMOD)

Efficient subgraph matching: Harmonizing dynamic programming, adap- tive matching order, and failing set together. InProceedings of the International Conference on Management of Data (SIGMOD). 1429–1446
[26]

Wook-Shin Han, Jinsoo Lee, and Jeong-Hoon Lee. 2013. Turboiso: towards ultrafast and robust subgraph isomorphism search in large graph databases. In Proceedings of the International Conference on Management of Data (SIGMOD). 337–348

2013
[27]

Huahai He and Ambuj K Singh. 2008. Graphs-at-a-time: query language and access methods for graph databases. InProceedings of the International Conference on Management of Data (SIGMOD). 405–418

2008
[28]

Craig A James. 2004. Daylight theory manual.http://www. daylight. com/dayhtml/doc/theory/theory. toc. html(2004)

2004
[29]

Haolin Jiang, Santosh Pandey, and Hang Liu. 2025. A Comprehensive Survey of Subgraph Matching:[Experiments & Analysis]. InProceedings of the International Conference on Management of Data (SIGMOD). 1–30

2025
[30]

Alpár Jüttner and Péter Madarasi. 2018. VF2++—An improved subgraph isomor- phism algorithm.Discrete Applied Mathematics242 (2018), 69–81

2018
[31]

Chathura Kankanamge, Siddhartha Sahu, Amine Mhedbhi, Jeremy Chen, and Semih Salihoglu. 2017. Graphflow: An active graph database. InProceedings of the International Conference on Management of Data (SIGMOD). 1695–1698

2017
[32]

Guy Karlebach and Ron Shamir. 2008. Modelling and analysis of gene regulatory networks.Nature Reviews Molecular Cell Biology9, 10 (2008), 770–780

2008
[33]

Foteini Katsarou, Nikos Ntarmos, and Peter Triantafillou. 2017. Subgraph query- ing with parallel use of query rewritings and alternative algorithms. InProceed- ings of the International Conference on Extending Database Technology (EDBT). 25–36

2017
[34]

Longbin Lai, Lu Qin, Xuemin Lin, and Lijun Chang. 2015. Scalable subgraph enumeration in mapreduce. InProceedings of the International Conference on Very Large Data Bases (PVLDB). 974–985

2015
[35]

Longbin Lai, Lu Qin, Xuemin Lin, Ying Zhang, Lijun Chang, and Shiyu Yang. 2016. Scalable distributed subgraph enumeration. InProceedings of the International Conference on Very Large Data Bases (PVLDB). 217–228

2016
[36]

Longbin Lai, Zhu Qing, Zhengyi Yang, Xin Jin, Zhengmin Lai, Ran Wang, Kongzhang Hao, Xuemin Lin, Lu Qin, Wenjie Zhang, et al. 2019. Distributed sub- graph matching on timely dataflow. InProceedings of the International Conference on Very Large Data Bases (PVLDB). 1099–1112

2019
[37]

Qiyan Li, Jeffrey Xu Yu, and Zongyan He. 2025. Subgraph Matching: A New Decomposition Based Approach. InProceedings of the International Conference on Very Large Data Bases (PVLDB). 4282–4294

2025
[38]

Yujia Li, Chenjie Gu, Thomas Dullien, Oriol Vinyals, and Pushmeet Kohli. 2019. Graph matching networks for learning the similarity of graph structured objects. InProceedings of the International Conference on Machine Learning (ICML). 3835– 3845

2019
[39]

Zijian Li, Xun Jian, Xiang Lian, and Lei Chen. 2018. An efficient probabilistic ap- proach for graph similarity search. InProceedings of the International Conference on Data Engineering (ICDE). 533–544

2018
[40]

Xiang Lian and Lei Chen. 2011. Efficient query answering in probabilistic RDF graphs. InProceedings of the International Conference on Management of Data (SIGMOD). 157–168

2011
[41]

Zhaoyu Lou, Jiaxuan You, Chengtao Wen, Arquimedes Canedo, Jure Leskovec, et al. 2020. Neural subgraph matching.arXiv preprint arXiv:2007.03092(2020)

work page arXiv 2020
[42]

Yujie Lu, Zhijie Zhang, and Weiguo Zheng. 2025. BSX: Subgraph Matching with Batch Backtracking Search. InProceedings of the International Conference on Management of Data (SIGMOD). 1–27

2025
[43]

Brian McFee and Gert Lanckriet. 2009. Partial order embedding with multiple kernels. InProceedings of the International Conference on Machine Learning (ICML). 721–728

2009
[44]

Amine Mhedhbi and Semih Salihoglu. 2019. Optimizing subgraph queries by combining binary and worst-case optimal joins. InProceedings of the International Conference on Very Large Data Bases (PVLDB). 1692–1704

2019
[45]

Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al
[46]

In Proceedings of the Advances in Neural Information Processing Systems (NeurIPS)

Pytorch: An imperative style, high-performance deep learning library. In Proceedings of the Advances in Neural Information Processing Systems (NeurIPS). 1–12
[47]

Charles R Qi, Hao Su, Kaichun Mo, and Leonidas J Guibas. 2017. PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation. InProceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR). 652–660

2017
[48]

Miao Qiao, Hao Zhang, and Hong Cheng. 2017. Subgraph matching: on com- pression and computation. InProceedings of the International Conference on Very Large Data Bases (PVLDB). 176–188

2017
[49]

Xuguang Ren and Junhu Wang. 2015. Exploiting vertex relationships in speeding up subgraph isomorphism over large graphs. InProceedings of the International Conference on Very Large Data Bases (PVLDB). 617–628

2015
[50]

Siddhartha Sahu, Amine Mhedhbi, Semih Salihoglu, Jimmy Lin, and M Tamer Özsu. 2017. The ubiquity of large graphs and surprising challenges of graph processing. InProceedings of the International Conference on Very Large Data Bases (PVLDB). 420–431

2017
[51]

Haichuan Shang, Ying Zhang, Xuemin Lin, and Jeffrey Xu Yu. 2008. Taming verification hardness: an efficient algorithm for testing subgraph isomorphism. InProceedings of the International Conference on Very Large Data Bases (PVLDB). 364–375

2008
[52]

Dennis Shasha, Jason TL Wang, and Rosalba Giugno. 2002. Algorithmics and ap- plications of tree and graph searching. InProceedings of the Principles of Database Systems (PODS). 39–52

2002
[53]

Shixuan Sun and Qiong Luo. 2020. In-memory subgraph matching: An in-depth study. InProceedings of the International Conference on Management of Data (SIGMOD). 1083–1098. 16

2020
[54]

Shixuan Sun, Xibo Sun, Yulin Che, Qiong Luo, and Bingsheng He. 2020. Rapid- match: A holistic approach to subgraph query processing. InProceedings of the International Conference on Very Large Data Bases (PVLDB). 176–188

2020
[55]

Zhao Sun, Hongzhi Wang, Haixun Wang, Bin Shao, and Jianzhong Li. 2012. Efficient Subgraph Matching on Billion Node Graphs. InProceedings of the Inter- national Conference on Very Large Data Bases (PVLDB). 788–799

2012
[56]

Damian Szklarczyk et al. 2015. STRING v10: protein–protein interaction net- works, integrated over the tree of life.Nucleic Acids Research43, D1 (2015), D447–D452

2015
[57]

Ivan Vendrov, Ryan Kiros, Sanja Fidler, and Raquel Urtasun. 2016. Order- embeddings of images and language. InProceedings of the International Conference on Learning Representations (ICLR). 1–12

2016
[58]

Hanchen Wang, Ying Zhang, Lu Qin, Wei Wang, Wenjie Zhang, and Xuemin Lin
[59]

InProceedings of the International Conference on Data Engineering (ICDE)

Reinforcement learning based query vertex ordering model for subgraph matching. InProceedings of the International Conference on Data Engineering (ICDE). 245–258
[60]

Stanley Wasserman and Katherine Faust. 1994. Social network analysis: Methods and applications. (1994)

1994
[61]

Duncan J Watts and Steven H Strogatz. 1998. Collective dynamics of ‘small- world’networks.Nature393, 6684 (1998), 440–442

1998
[62]

Qi Wen, Yutong Ye, Xiang Lian, and Mingsong Chen. 2025. S3AND: Efficient Subgraph Similarity Search Under Aggregated Neighbor Difference Semantics. InProceedings of the International Conference on Very Large Data Bases (PVLDB). 3708–3720

2025
[63]

Kun Xu, Liwei Wang, Mo Yu, Yansong Feng, Yan Song, Zhiguo Wang, and Dong Yu. 2019. Cross-lingual knowledge graph alignment via graph matching neural network.arXiv preprint arXiv:1905.11605(2019)

work page arXiv 2019
[64]

Xifeng Yan, Hong Cheng, Jiawei Han, and Philip S Yu. 2008. Mining significant graph patterns by leap search. InProceedings of the International Conference on Management of Data (SIGMOD). 433–444

2008
[65]

Xifeng Yan, Philip S Yu, and Jiawei Han. 2004. Graph indexing: a frequent structure-based approach. InProceedings of the International Conference on Man- agement of Data (SIGMOD). 335–346

2004
[66]

Linglin Yang, Lei Zou, and Chunshan Zhao. 2025. NeuSO: Neural Optimizer for Subgraph Queries. InProceedings of the International Conference on Management of Data (SIGMOD). 1–28

2025
[67]

Yutong Ye, Xiang Lian, and Mingsong Chen. 2024. Efficient Exact Subgraph Matching via GNN-based Path Dominance Embedding. InProceedings of the International Conference on Very Large Data Bases (PVLDB). 1628–1641

2024
[68]

Yutong Ye, Xiang Lian, Nan Zhang, and Mingsong Chen. 2025. Continuous Sub- graph Matching via Cost-Model-based Dynamic Vertex Dominance Embeddings. InProceedings of the International Conference on Management of Data (SIGMOD). 1–27

2025
[69]

Manzil Zaheer, Satwik Kottur, Siamak Ravanbakhsh, Barnabas Poczos, Ruslan Salakhutdinov, and Alexander Smola. 2017. Deep Sets. InAdvances in Neural Information Processing Systems (NeurIPS), Vol. 30

2017
[70]

Nan Zhang, Yutong Ye, Xiang Lian, and Mingsong Chen. 2024. Top- 𝐿 Most Influential Community Detection Over Social Networks. InProceedings of the International Conference on Data Engineering (ICDE). 5767–5779

2024
[71]

Peixiang Zhao and Jiawei Han. 2010. On graph query optimization in large networks. InProceedings of the International Conference on Very Large Data Bases (PVLDB). 340–351. 17

2010