pith. sign in

arxiv: 2605.26291 · v1 · pith:VLSHFGHHnew · submitted 2026-05-25 · 💻 cs.PL · cs.DB

Geo: A Query Rewrite Framework for Graph Pattern Mining

Nazanin Yousefian , Kasra Jamshidi , Keval Vora , Anders Miltner This is my paper

Pith reviewed 2026-06-29 19:13 UTC · model grok-4.3

classification 💻 cs.PL cs.DB
keywords graph pattern miningquery optimizationrewrite rulesequality saturationsubgraph isomorphismprogrammable optimizerprovenance tracking
0
0 comments X

The pith

Geo rewrites graph pattern queries using equivalences discovered through equality saturation to achieve up to 99 percent cost reduction.

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

Geo supplies a language for writing pattern equivalences as rewrite rules that a system can apply automatically to graph mining queries. The system keeps canonical forms of patterns during equality saturation so that isomorphic variants do not block further rewrites. Embedded reconstructability tracks how each rewritten pattern can be turned back into the original output, preserving semantics across rule applications. Evaluation shows that composing these rules yields novel equivalences and lowers execution cost by as much as 99 percent relative to earlier hand-tuned queries. The same machinery also speeds up two practical tasks, approximate matching and quasi-clique mining, by up to 71 percent.

Core claim

Geo is a programmable optimizer that accepts user-defined rewrite rules expressing pattern equivalences, maintains canonical representations during equality saturation to avoid syntactic duplication of isomorphic patterns, and applies embedded reconstructability to track provenance so that every optimized query remains semantically equivalent to the input query.

What carries the argument

Equality saturation over canonical pattern representations together with embedded reconstructability (EmRec) for provenance tracking.

If this is right

  • Complex compositions of simple rules can produce previously unknown equivalences that prior hand-written optimizers missed.
  • Queries optimized by Geo run with up to 99 percent lower cost than the best queries reported in earlier work.
  • The same optimizer improves two distinct mining tasks, approximate pattern matching and quasi-clique mining, by up to 71 percent.
  • Developers can add new equivalences over time without manually resolving interactions among existing rules.
  • Correctness is maintained by construction through provenance tracking rather than post-hoc verification.

Where Pith is reading between the lines

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

  • The approach could be ported to other domains that rely on pattern matching if suitable rewrite rules and a canonical form are defined for those patterns.
  • Continuous addition of rules might eventually saturate the search space, making further manual rule writing unnecessary for some workloads.
  • The framework's separation of rule authoring from interaction management could reduce the expertise needed to maintain production graph-mining pipelines.

Load-bearing premise

The supplied rewrite rules plus the canonical-representation and EmRec mechanisms together preserve the original query semantics on every input graph.

What would settle it

Execute an optimized query produced by Geo on a concrete input graph whose results are already known from the unoptimized version; any mismatch in output sets falsifies the claim that semantics are preserved.

Figures

Figures reproduced from arXiv: 2605.26291 by Anders Miltner, Kasra Jamshidi, Keval Vora, Nazanin Yousefian.

Figure 1
Figure 1. Figure 1: Example rewrite rules in Subgraph Morphing (a) and ESCAPE (b). Dashed lines represent anti-edges. mining are primarily based on solving the subgraph isomorphism problem. In essence, by charac￾terizing these substructures of interest as subgraphs, graph mining systems solve the subgraph isomorphism problem. Subgraph isomorphism is an NP-complete problem, developing efficient subgraph matching algorithms is … view at source ↗
Figure 2
Figure 2. Figure 2: Generalized rewrite rule of Subgraph Morphing. For any pattern 𝑥, 𝑥 𝑉 denotes the pattern with anti-edges added to each disconnected edge. The term 𝑞 ⊃ 𝑝 means that 𝑞 is a super-pattern of 𝑝 with the same number of vertices. The function 𝜙 (𝑝, 𝑞) represents the number of isomorphisms of 𝑝 within 𝑞. together represents their overall distribution. On the other hand, Collective reconstructability requires the… view at source ↗
Figure 3
Figure 3. Figure 3: Quasi-clique mining example, 𝛾 = 0.8 # = 5,148 p1 Rewritten Pattern Graph Mining Matching Query Problem Pattern Matching Query List of Coefficients Optimization via Rewrite Rules Cost Model p1 p2 p3 1 2 3 Pattern Matching Engine Rewrite Rules Data Graph p1 p2 p3 p1 p4 p5 F # = 3,392 p2 # = 4,379 p3 Individual Subgraph Mining [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Subgraph mining example. 2.1.3 End-to-End Examples of Graph Mining & Pattern Matching Queries. We present two examples of graph mining problems, focusing on their translation to pattern matching queries, which are then optimized via rewrite rules to generate equivalent pattern matching queries for the downstream pattern matching engine. To showcase the key differences in various requirements, we show: (a) … view at source ↗
Figure 5
Figure 5. Figure 5: Queries for Quasi-Clique Mining and Subgraph mining. [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Formal grammar of the pattern matching query language. The meta-variable [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Semantics of the graph pattern mining language. Given a concrete data graph [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Built-In Rewrite Rules. Rules marked with [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Characteristics of the two sets of rewrite rules, [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Patterns used in evaluation along with their relative execution time (seconds) used for optimization. [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Execution time (seconds) of alternative pattern queries generated by [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Execution time (seconds) of alternative pattern queries generated by [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Equivalences generated for 𝑝13 input by Geo, Subgraph Morphing and ESCAPE along with their run times. 𝐹1 filters triangle nodes with external connections. 𝐹2 filters triangle edges shared with other triangles. Geo Subgraph Morphing ESCAPE Pattern(𝑝18) Union(Count((𝜋18, 1),Pattern(𝑝1,𝐹3)), Pattern(𝑝18) Union(Count((𝜋18, 1),Pattern(𝑝1,𝐹3)), Count( (𝜋18, −4) + (𝜋19, −2), Count((𝜋18, −4),Pattern(𝑝10))) Patter… view at source ↗
Figure 14
Figure 14. Figure 14: Equivalences generated for {𝑝18, 𝑝19} input by Geo, Subgraph Morphing and ESCAPE along with their run times. 𝐹2 filters triangle edges shared with other triangles, 𝐹3 filters triangle nodes with external connections of at least degree 2, and 𝐹4 filters edges where both endpoints have external connections. Geo Subgraph Morphing ESCAPE Pattern(𝑝12) Union( Union( Pattern(𝑝12) Count((𝜋12, 1) + (𝜋24, −2),Patte… view at source ↗
Figure 15
Figure 15. Figure 15: Equivalences generated for {𝑝12, 𝑝23, 𝑝24} input by Geo, Subgraph Morphing and ESCAPE along with their run times. 𝐹2 filters triangle edges shared with other triangles, 𝐹7 filters triangle nodes where two are connected in an external triangle and the third has an external connection, and 𝐹8 filters 4-cycle nodes with external connections. Moreover, using Geo achieves a speedup of up to 70× compared to ESC… view at source ↗
Figure 16
Figure 16. Figure 16: Execution time (seconds) for batched-individual and batched-collective queries on [PITH_FULL_IMAGE:figures/full_fig_p020_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Equivalences generated for {𝑝6, 𝑝11, 𝑝15} by Geo for individual and collective results along with their costs. 𝐹1 filters triangle nodes with external connections of at least degree 2, and 𝐹2 filters triangle edges shared with other triangles. batched pattern matching query {𝑝6, 𝑝11, 𝑝15} for the two EmRec choices. Using unique reconstruc￾tion paths for each pattern prevents Geo from detecting and elimina… view at source ↗
Figure 18
Figure 18. Figure 18: (a) Execution time (seconds) of alternative patterns generated for [PITH_FULL_IMAGE:figures/full_fig_p021_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Approximate pattern mining queries with edit distance [PITH_FULL_IMAGE:figures/full_fig_p022_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Execution Time (seconds) for approximate pattern mining with collective reconstructibility. [PITH_FULL_IMAGE:figures/full_fig_p022_20.png] view at source ↗
Figure 22
Figure 22. Figure 22: Quasi-clique mining queries and the set of patterns in translated batched pattern matching queries. [PITH_FULL_IMAGE:figures/full_fig_p023_22.png] view at source ↗
Figure 24
Figure 24. Figure 24: Formal grammar of opaque matchers. [[(Count(𝜑𝑃𝑀𝑄 (Π),𝜑𝑃𝑀𝑄 (𝑄 ′ ))]]𝐺 (𝜋) = [[𝜑𝑃𝑀𝑄 (Π)]] (𝜋1) × [[𝜑𝑃𝑀𝑄 (𝑄 ′ )]]𝐺 (𝜋2) where 𝜋1𝜋2 = 𝜋, which by IH equals [[Π]] (𝜋1) × [[𝑄 ′ ]]𝐺 (𝜋2) = [[Count(Π,𝑄 ′)]] (𝜋), as desired. [Case 3:] 𝑄 = Pattern(𝑃,𝐹). [[𝜑𝑃𝑀𝑄 (Pattern(𝑃,𝐹))]]𝐺 = [[(Pattern(𝜑𝑃𝑀𝑄 (𝑃),𝐹)]]𝐺 by the definition of 𝜑𝑃𝑀𝑄 (the 𝐹 variables are considered semantic and ignored by the canonizer). Let 𝜋 be an a… view at source ↗
read the original abstract

Graph pattern mining is important for analyzing graph data. Graph mining systems typically require answering pattern matching queries, which involve solving the NP-complete subgraph isomorphism problem. To address this, domain experts often develop custom optimization strategies based on exploiting substructural similarities across different patterns. While these optimizers can be effective, their development is challenging, limiting the exploration of interactions between different optimization strategies and restricts experts from continuously improving the optimizers -- such as by incorporating additional custom or general pattern-based equivalences over time. We present a programmable pattern matching query optimizer called Geo, which automatically manages the interactions between various equivalences, ensures the optimizations maintain correctness of results, and simplifies the management of substructure equivalences. Geo exposes a simple but flexible language for expressing pattern equivalences as rewrite rules. By maintaining canonical representations of generated patterns during equality saturation, Geo avoids issues arising from syntactic differences in isomorphic patterns. Additionally, we develop embedded reconstructablility (EmRec) that tracks provenance across equivalences to ensure various reconstructability needs of desired outputs. Our evaluation demonstrates that Geo can discover novel query equivalences through complex composition of various rewrite rules, enabling our optimized queries to achieve a cost reduction of up to 99% compared to the queries in prior work. We further test Geo's effectiveness at speeding up practical graph mining problems by using it in two representative case studies -- approximate pattern matching and quasi-clique mining, and find it is highly effective at optimizing these tasks, enabling cost reductions of up to 71%.

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.

Referee Report

0 major / 3 minor

Summary. The paper introduces Geo, a programmable optimizer for graph pattern matching queries in graph mining. It provides a language for expressing pattern equivalences as rewrite rules, uses equality saturation with canonical representations to handle isomorphic patterns, and introduces embedded reconstructability (EmRec) to track provenance and preserve semantics. The central claims are that Geo discovers novel equivalences via rule composition and achieves up to 99% cost reduction versus prior work, with up to 71% reductions demonstrated in case studies on approximate pattern matching and quasi-clique mining.

Significance. If the evaluation and semantic-preservation mechanisms hold, Geo would provide a valuable extensible framework for composing optimizations in an NP-hard domain, reducing reliance on hand-crafted optimizers and enabling systematic exploration of equivalences. The use of canonical forms and provenance tracking addresses practical challenges in equality saturation for this setting.

minor comments (3)
  1. The abstract and introduction claim 'up to 99% cost reduction' and 'novel query equivalences' but the evaluation section should explicitly define the cost model (e.g., which operations are counted) and list the exact baseline queries from prior work for reproducibility.
  2. Section on EmRec should include a small worked example showing how provenance is tracked across a multi-rule composition to confirm that reconstructability constraints are enforced without false negatives.
  3. The paper would benefit from a table summarizing the rewrite rules used in the case studies, including their source (custom vs. general) and how many were newly discovered by Geo.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper describes a systems framework (Geo) for query rewriting via equality saturation and EmRec provenance tracking. All load-bearing claims are empirical: evaluation shows novel equivalences discovered via rule composition and measured cost reductions (up to 99%). No derivation chain, equations, or fitted parameters are presented that reduce to inputs by construction. Canonical representations and EmRec are design mechanisms whose semantic preservation is asserted and tested externally via benchmarks, not defined in terms of the target results. No self-citation load-bearing steps or uniqueness theorems appear in the abstract or described approach.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides insufficient detail to identify concrete free parameters, axioms, or invented entities; no specific numbers or unproven assumptions are stated.

pith-pipeline@v0.9.1-grok · 5807 in / 1027 out tokens · 39698 ms · 2026-06-29T19:13:19.746645+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

69 extracted references · 62 canonical work pages · 1 internal anchor

  1. [1]

    Distributed evaluation of subgraph queries using worst-case optimal low-memory dataflows. Proc. VLDB Endow. 11, 6 (Feb. 2018), 691–704. https://doi.org/10.14778/ 3199517.3199520 Nikos Armenatzoglou, Sanuj Basu, Naga Bhanoori, Mengchu Cai, Naresh Chainani, Kiran Chinta, Venkatraman Govindaraju, Todd J. Green, Monish Gupta, Sebastian Hillig, Eric Hotinger, ...

    work page arXiv 2018

  2. [2]

    In Proceedings of the 2022 International Conference on Management of Data (Philadelphia, PA, USA) (SIGMOD ’22)

    Amazon Redshift Re-invented. In Proceedings of the 2022 International Conference on Management of Data (Philadelphia, PA, USA) (SIGMOD ’22). Association for Computing Machinery, New York, NY, USA, 2205–2217. https://doi.org/10.1145/3514221.3526045 Bibek Bhattarai, Hang Liu, and H. Howie Huang

    work page doi:10.1145/3514221.3526045 2022

  3. [3]

    In Proceedings of the 2019 International Conference on Management of Data (Amsterdam, Netherlands) (SIGMOD ’19)

    CECI: Compact Embedding Cluster Index for Scalable Subgraph Matching. In Proceedings of the 2019 International Conference on Management of Data (Amsterdam, Netherlands) (SIGMOD ’19). 1447–1462. https://doi.org/10.1145/3299869.3300086 Fei Bi, Lijun Chang, Xuemin Lin, Lu Qin, and Wenjie Zhang

    work page doi:10.1145/3299869.3300086 2019

  4. [4]

    In Proceedings of the 2016 International Conference on Management of Data (San Francisco, CA, USA) (SIGMOD ’16)

    Efficient Subgraph Matching by Postponing Cartesian Products. In Proceedings of the 2016 International Conference on Management of Data (San Francisco, CA, USA) (SIGMOD ’16). 1199–1214. https://doi.org/10.1145/2882903.2915236 Mauro Brunato, Holger H Hoos, and Roberto Battiti

    work page doi:10.1145/2882903.2915236 2016

  5. [5]

    Exact Quantum Algorithms for the Leader Election Problem,

    On effectively finding maximal quasi-cliques in graphs. In International conference on learning and intelligent optimization . Springer, 41–55. https://doi.org/10.1007/978-3-540- 92695-5_4 Dongbo Bu, Yi Zhao, Lun Cai, Hong Xue, Xiaopeng Zhu, Hongchao Lu, Jingfen Zhang, Shiwei Sun, Lunjiang Ling, Nan Zhang, et al

    work page doi:10.1007/978-3-540-

  6. [6]

    Nucleic acids research 31, 9 (2003), 2443–2450

    Topological structure analysis of the protein–protein interaction network in budding yeast. Nucleic acids research 31, 9 (2003), 2443–2450. https://doi.org/10.1093/nar/gkg340 Peter Buneman, Sanjeev Khanna, and Tan Wang-Chiew

    work page doi:10.1093/nar/gkg340 2003

  7. [7]

    In Database Theory — ICDT 2001 , Jan Van den Bussche and Victor Vianu (Eds.)

    Why and Where: A Characterization of Data Provenance. In Database Theory — ICDT 2001 , Jan Van den Bussche and Victor Vianu (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 316–330. https://doi.org/10.1007/3-540-44503-X_20 Walter Cai, Magdalena Balazinska, and Dan Suciu

    work page doi:10.1007/3-540-44503-x_20 2001

  8. [8]

    In Proceedings of the 2019 International Conference on Management of Data (Amsterdam, Netherlands) (SIGMOD ’19)

    Pessimistic Cardinality Estimation: Tighter Upper Bounds for Intermediate Join Cardinalities. In Proceedings of the 2019 International Conference on Management of Data (Amsterdam, Netherlands) (SIGMOD ’19). 18–35. https://doi.org/10.1145/3299869.3319894 David Cao, Rose Kunkel, Chandrakana Nandi, Max Willsey, Zachary Tatlock, and Nadia Polikarpova

    work page doi:10.1145/3299869.3319894 2019

  9. [9]

    babble: Learning Better Abstractions with E-Graphs and Anti-unification. Proc. ACM Program. Lang. 7, POPL, Article 14 (Jan. 2023), 29 pages. https://doi.org/10.1145/3571207 Joanna Che, Kasra Jamshidi, and Keval Vora

    work page doi:10.1145/3571207 2023

  10. [10]

    InProceedings of the Nineteenth European Conference on Computer Systems (Athens, Greece) (EuroSys ’24)

    Contigra: Graph Mining with Containment Constraints. InProceedings of the Nineteenth European Conference on Computer Systems (Athens, Greece) (EuroSys ’24). Association for Computing Machinery, New York, NY, USA, 50–65. https://doi.org/10.1145/3627703.3629589 Jeremy Chen, Yuqing Huang, Mushi Wang, Semih Salihoglu, and Ken Salem

    work page doi:10.1145/3627703.3629589

  11. [11]

    Proceedings of the VLDB Endowment 15, 8 (April 2022), 1533–1545

    Accurate summary-based cardinality estimation through the lens of cardinality estimation graphs. Proceedings of the VLDB Endowment 15, 8 (April 2022), 1533–1545. https://doi.org/10.14778/3529337.3529339 Jingji Chen and Xuehai Qian

    work page doi:10.14778/3529337.3529339 2022

  12. [12]

    In Proceedings of the 28th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 1 (Vancouver, BC, Canada) (ASPLOS 2023)

    DecoMine: A Compilation-Based Graph Pattern Mining System with Pattern Decompo- sition. In Proceedings of the 28th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 1 (Vancouver, BC, Canada) (ASPLOS 2023). 47–61. https://doi.org/10.1145/3567955.3567956 Jingji Chen and Xuehai Qian

    work page doi:10.1145/3567955.3567956 2023

  13. [13]

    In Proceedings of the 28th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2 (Vancouver, BC, Canada) (ASPLOS 2023)

    Khuzdul: Efficient and Scalable Distributed Graph Pattern Mining Engine. In Proceedings of the 28th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2 (Vancouver, BC, Canada) (ASPLOS 2023). 413–426. https://doi.org/10.1145/3575693.3575743 Xuhao Chen and Arvind

    work page doi:10.1145/3575693.3575743 2023

  14. [14]

    Association for Computing Machinery, New York, NY, USA, 378–391

    Geo: A Query Rewrite Framework for Graph Pattern Mining 131:27 USA) (ICS ’21). Association for Computing Machinery, New York, NY, USA, 378–391. https://doi.org/10.1145/3447818. 3460359 Jianyi Cheng, Samuel Coward, Lorenzo Chelini, Rafael Barbalho, and Theo Drane

    work page doi:10.1145/3447818

  15. [15]

    InProceedings of the 29th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2 (La Jolla, CA, USA) (ASPLOS ’24)

    SEER: Super-Optimization Explorer for High-Level Synthesis using E-graph Rewriting. InProceedings of the 29th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2 (La Jolla, CA, USA) (ASPLOS ’24). Association for Computing Machinery, New York, NY, USA, 1029–1044. https://doi.org/10.1145/3620665.36...

    work page doi:10.1145/3620665.3640392

  16. [16]

    In 2022 IEEE 29th Symposium on Computer Arithmetic (ARITH)

    Automatic Datapath Optimization using E-Graphs . In 2022 IEEE 29th Symposium on Computer Arithmetic (ARITH) . IEEE Computer Society, Los Alamitos, CA, USA, 43–50. https://doi.org/10.1109/ARITH54963.2022.00016 Vinicius Dias, Carlos H. C. Teixeira, Dorgival Guedes, Wagner Meira, and Srinivasan Parthasarathy

    work page doi:10.1109/arith54963.2022.00016 2022

  17. [17]

    In Proceedings of the 2019 International Conference on Management of Data (Amsterdam, Netherlands) (SIGMOD ’19)

    Fractal: A General-Purpose Graph Pattern Mining System. In Proceedings of the 2019 International Conference on Management of Data (Amsterdam, Netherlands) (SIGMOD ’19). Association for Computing Machinery, New York, NY, USA, 1357–1374. https://doi.org/10.1145/3299869.3319875 Rui Dong, Jie Liu, Yuxuan Zhu, Cong Yan, Barzan Mozafari, and Xinyu Wang

    work page doi:10.1145/3299869.3319875 2019

  18. [18]

    SlabCity: Whole-Query Optimization Using Program Synthesis. Proc. VLDB Endow. 16, 11 (July 2023), 3151–3164. https://doi.org/10.14778/3611479.3611515 Mohammed Elseidy, Ehab Abdelhamid, Spiros Skiadopoulos, and Panos Kalnis

    work page doi:10.14778/3611479.3611515 2023

  19. [19]

    GraMi: frequent subgraph and pattern mining in a single large graph. Proc. VLDB Endow. 7, 7 (March 2014), 517–528. https://doi.org/10.14778/2732286.2732289 John Nathan Foster

    work page doi:10.14778/2732286.2732289 2014

  20. [20]

    In 2023 USENIX Annual Technical Conference (USENIX ATC

    Cyclosa: Redundancy-Free Graph Pattern Mining via Set Dataflow. In 2023 USENIX Annual Technical Conference (USENIX ATC

    2023

  21. [21]

    In Proceedings of the 2019 International Conference on Management of Data (Amsterdam, Netherlands) (SIGMOD ’19)

    Efficient Subgraph Matching: Harmonizing Dynamic Programming, Adaptive Matching Order, and Failing Set Together. In Proceedings of the 2019 International Conference on Management of Data (Amsterdam, Netherlands) (SIGMOD ’19). 1429–1446. https://doi.org/10. 1145/3299869.3319880 Wook-Shin Han, Jinsoo Lee, and Jeong-Hoon Lee

    work page arXiv 2019

  22. [22]

    In Proceedings of the 2013 International Conference on Management of Data (New York, NY, USA) (SIGMOD ’13)

    TurboISO: Towards Ultrafast and Robust Subgraph Isomorphism Search in Large Graph Databases. In Proceedings of the 2013 International Conference on Management of Data (New York, NY, USA) (SIGMOD ’13). 337–348. https://doi.org/10.1145/2463676.2465300 John Hopcroft, Omar Khan, Brian Kulis, and Bart Selman

    work page doi:10.1145/2463676.2465300 2013

  23. [23]

    Proceedings of the National Academy of Sciences 101, suppl_1 (2004), 5249–5253

    Tracking evolving communities in large linked networks. Proceedings of the National Academy of Sciences 101, suppl_1 (2004), 5249–5253. https://doi.org/10.1073/pnas.0307750100 Haiyan Hu, Xifeng Yan, Yu Huang, Jiawei Han, and Xianghong Jasmine Zhou

    work page doi:10.1073/pnas.0307750100 2004

  24. [24]

    Bioinformatics 21, suppl_1 (2005), i213–i221

    Mining coherent dense subgraphs across massive biological networks for functional discovery. Bioinformatics 21, suppl_1 (2005), i213–i221. https: //doi.org/10.1093/bioinformatics/bti1049 Pan Hu and Boris Motik

    work page doi:10.1093/bioinformatics/bti1049 2005

  25. [25]

    ACM Transactions on Database Systems 49, 3, Article 12 (Sept

    Accurate Sampling-Based Cardinality Estimation for Complex Graph Queries. ACM Transactions on Database Systems 49, 3, Article 12 (Sept. 2024), 46 pages. https://doi.org/10.1145/3689209 Anand Padmanabha Iyer, Zaoxing Liu, Xin Jin, Shivaram Venkataraman, Vladimir Braverman, and Ion Stoica

    work page doi:10.1145/3689209 2024

  26. [26]

    In Proceedings of the Fifteenth European Conference on Computer Systems (Heraklion, Greece) (EuroSys ’20)

    Peregrine: A Pattern-Aware Graph Mining System. In Proceedings of the Fifteenth European Conference on Computer Systems (Heraklion, Greece) (EuroSys ’20). Article 13, 16 pages. https://doi.org/10.1145/3342195.3387548 Kasra Jamshidi and Keval Vora

    work page doi:10.1145/3342195.3387548

  27. [27]

    SIGOPS Oper

    A Deeper Dive into Pattern-Aware Subgraph Exploration with PEREGRINE. SIGOPS Oper. Syst. Rev. 55, 1 (June 2021), 1–10. https://doi.org/10.1145/3469379.3469381 Kasra Jamshidi, Harry Xu, and Keval Vora

    work page doi:10.1145/3469379.3469381 2021

  28. [28]

    In Proceedings of the Eighteenth European Conference on Computer Systems (Rome, Italy) (EuroSys ’23)

    Accelerating Graph Mining Systems with Subgraph Morphing. In Proceedings of the Eighteenth European Conference on Computer Systems (Rome, Italy) (EuroSys ’23). 162–181. https: //doi.org/10.1145/3552326.3567489 Tommi Junttila and Petteri Kaski

    work page doi:10.1145/3552326.3567489

  29. [29]

    Engineering an efficient canonical labeling tool for large and sparse graphs. In Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments and the Fourth Workshop on Analytic Algorithms and Combinatorics, David Applegate, Gerth Stølting Brodal, Daniel Panario, and Robert Sedgewick (Eds.). SIAM, 135–149. https://doi.org/10.1137/1.978161197...

    work page doi:10.1137/1.9781611972870.13

  30. [30]

    In Proceedings of the 2016 International Conference on Management of Data (San Francisco, CA, USA) (SIGMOD ’16)

    DUALSIM: Parallel Subgraph Enumeration in a Massive Graph on a Single Machine. In Proceedings of the 2016 International Conference on Management of Data (San Francisco, CA, USA) (SIGMOD ’16). 1231–1245. https: //doi.org/10.1145/2882903.2915209 Kyoungmin Kim, Jisung Jung, In Seo, Wook-Shin Han, Kangwoo Choi, and Jaehyok Chong

    work page doi:10.1145/2882903.2915209 2016

  31. [31]

    In Proceedings of the 2022 International Conference on Management of Data (Philadelphia, PA, USA) (SIGMOD ’22)

    Learned Cardinality Estimation: An In-depth Study. In Proceedings of the 2022 International Conference on Management of Data (Philadelphia, PA, USA) (SIGMOD ’22). 1214–1227. https://doi.org/10.1145/3514221.3526154 Proc. ACM Program. Lang., Vol. 10, No. OOPSLA1, Article

    work page doi:10.1145/3514221.3526154 2022

  32. [32]

    In Proceedings of the 31st ACM SIGPLAN International Conference on Compiler Construction (Seoul, South Korea) (CC 2022)

    Caviar: an e-graph based TRS for automatic code optimization. In Proceedings of the 31st ACM SIGPLAN International Conference on Compiler Construction (Seoul, South Korea) (CC 2022). Association for Computing Machinery, New York, NY, USA, 54–64. https://doi.org/10.1145/3497776.3517781 Longbin Lai, Lu Qin, Xuemin Lin, and Lijun Chang

    work page doi:10.1145/3497776.3517781 2022

  33. [33]

    Proceedings of the VLDB Endowment 8, 10 (June 2015), 974–985

    Scalable Subgraph Enumeration in MapReduce. Proceedings of the VLDB Endowment 8, 10 (June 2015), 974–985. https://doi.org/10.14778/2794367.2794368 Longbin Lai, Lu Qin, Xuemin Lin, Ying Zhang, Lijun Chang, and Shiyu Yang

    work page doi:10.14778/2794367.2794368 2015

  34. [34]

    Proceedings of the VLDB Endowment 10, 3 (Nov

    Scalable Distributed Subgraph Enumeration. Proceedings of the VLDB Endowment 10, 3 (Nov. 2016), 217–228. https://doi.org/10.14778/3021924.3021937 John R Levine, Tony Mason, and Doug Brown

    work page doi:10.14778/3021924.3021937 2016

  35. [35]

    Online learning: A comprehensive survey

    Uncovering the overlapping community structure of complex networks by maximal cliques. Physica A: Statistical Mechanics and its Applications 415 (2014), 398–406. https://doi.org/10.1016/j. physa.2014.08.025 Guimei Liu and Limsoon Wong

    work page doi:10.1016/j 2014

  36. [36]

    In Joint European conference on machine learning and knowledge discovery in databases

    Effective pruning techniques for mining quasi-cliques. In Joint European conference on machine learning and knowledge discovery in databases . Springer, 33–49. https://doi.org/10.1007/978-3-540-87481-2_3 Justin Lubin, Jeremy Ferguson, Kevin Ye, Jacob Yim, and Sarah E. Chasins

    work page doi:10.1007/978-3-540-87481-2_3

  37. [37]

    Equivalence by Canonicalization for Synthesis-Backed Refactoring. Proc. ACM Program. Lang. 8, PLDI, Article 223 (June 2024), 26 pages. https://doi.org/10. 1145/3656453 Dror Marcus and Yuval Shavitt

    2024

  38. [38]

    Computer Networks 56, 2 (Feb

    RAGE: A Rapid Graphlet Enumerator for Large Networks. Computer Networks 56, 2 (Feb. 2012), 810–819. https://doi.org/10.1016/j.comnet.2011.08.019 Daniel Mawhirter and Bo Wu

    work page doi:10.1016/j.comnet.2011.08.019 2012

  39. [39]

    In Proceedings of the 27th ACM Symposium on Operating Systems Principles (Huntsville, ON, Canada) (SOSP ’19)

    AutoMine: Harmonizing High-Level Abstraction and High Performance for Graph Mining. In Proceedings of the 27th ACM Symposium on Operating Systems Principles (Huntsville, ON, Canada) (SOSP ’19). 509–523. https://doi.org/10.1145/3341301.3359633 Ine Melckenbeeck, Pieter Audenaert, Didier Colle, and Mario Pickavet

    work page doi:10.1145/3341301.3359633

  40. [40]

    Bioinformatics 34, 8 (Nov

    Efficiently Counting All Orbits of Graphlets of Any Order in a Graph Using Autogenerated Equations. Bioinformatics 34, 8 (Nov. 2017), 1372–1380. https://doi.org/10. 1093/bioinformatics/btx758 Ine Melckenbeeck, Pieter Audenaert, Thomas Van Parys, Yves Van De Peer, Didier Colle, and Mario Pickavet

    2017

  41. [41]

    BMC Bioinformatics 20, 1 (Jan

    Optimising Orbit Counting of Arbitrary Order by Equation Selection. BMC Bioinformatics 20, 1 (Jan. 2019). https: //doi.org/10.1186/s12859-018-2483-9 Amine Mhedhbi and Semih Salihoglu

    work page doi:10.1186/s12859-018-2483-9 2019

  42. [42]

    Proceedings of the VLDB Endowment 12, 11 (July 2019), 1692–1704

    Optimizing Subgraph Queries by Combining Binary and Worst-Case Optimal Joins. Proceedings of the VLDB Endowment 12, 11 (July 2019), 1692–1704. https://doi.org/10.14778/3342263.3342643 Ron Milo, Shai Shen-Orr, Shalev Itzkovitz, Nadav Kashtan, Dmitri Chklovskii, and Uri Alon

    work page doi:10.14778/3342263.3342643 2019

  43. [43]

    Science 298, 5594 (2002), 824–827

    Network Motifs: Simple Building Blocks of Complex Networks. Science 298, 5594 (2002), 824–827. https://doi.org/10.1126/science.298.5594.824 Greg Nelson and Derek C. Oppen

    work page doi:10.1126/science.298.5594.824 2002

  44. [44]

    Fast Decision Procedures Based on Congruence Closure. J. ACM 27, 2 (April 1980), 356–364. https://doi.org/10.1145/322186.322198 Julie L. Newcomb, Andrew Adams, Steven Johnson, Rastislav Bodik, and Shoaib Kamil

    work page doi:10.1145/322186.322198 1980

  45. [45]

    ACM Program

    Verifying and improving Halide’s term rewriting system with program synthesis.Proc. ACM Program. Lang. 4, OOPSLA, Article 166 (Nov. 2020), 28 pages. https://doi.org/10.1145/3428234 Pavel Panchekha, Alex Sanchez-Stern, James R. Wilcox, and Zachary Tatlock

    work page doi:10.1145/3428234 2020

  46. [46]

    In Proceedings of the 36th ACM SIGPLAN Conference on Programming Language Design and Implementation (Portland, OR, USA) (PLDI ’15)

    Automatically improving accuracy for floating point expressions. In Proceedings of the 36th ACM SIGPLAN Conference on Programming Language Design and Implementation (Portland, OR, USA) (PLDI ’15). Association for Computing Machinery, New York, NY, USA, 1–11. https://doi.org/10.1145/2737924.2737959 Yeonsu Park, Seongyun Ko, Sourav S. Bhowmick, Kyoungmin Ki...

    work page doi:10.1145/2737924.2737959

  47. [47]

    In Proceedings of the 2020 ACM SIGMOD International Conference on Management of Data (Portland, OR, USA) (SIGMOD ’20)

    G-CARE: A Framework for Performance Benchmarking of Cardinality Estimation Techniques for Subgraph Matching. In Proceedings of the 2020 ACM SIGMOD International Conference on Management of Data (Portland, OR, USA) (SIGMOD ’20). 1099–1114. https://doi.org/10.1145/3318464.3389702 Benedict Paten, Adam M Novak, Jordan M Eizenga, and Erik Garrison

    work page doi:10.1145/3318464.3389702 2020

  48. [48]

    Genome research 27, 5 (2017), 665–676

    Genome graphs and the evolution of genome inference. Genome research 27, 5 (2017), 665–676. https://doi.org/10.1101/gr.214155.116 Ali Pinar, Comandur Seshadhri, and Vaidyanathan Vishal

    work page doi:10.1101/gr.214155.116 2017

  49. [49]

    In Proceedings of the 26th International Conference on World Wide Web (Perth, Australia) (WWW ’17)

    ESCAPE: Efficiently Counting All 5-Vertex Subgraphs. In Proceedings of the 26th International Conference on World Wide Web (Perth, Australia) (WWW ’17). 1431–1440. https: //doi.org/10.1145/3038912.3052597 Miao Qiao, Hao Zhang, and Hong Cheng

    work page doi:10.1145/3038912.3052597

  50. [50]

    Proceedings of the VLDB Endowment 11, 2 (Oct

    Subgraph Matching: On Compression and Computation. Proceedings of the VLDB Endowment 11, 2 (Oct. 2017), 176–188. https://doi.org/10.14778/3149193.3149198 VN Redko

    work page doi:10.14778/3149193.3149198 2017

  51. [51]

    Proceedings of the VLDB Endowment 12, 11 (2019), 1344–1356

    Fast and Robust Distributed Subgraph Enumeration. Proceedings of the VLDB Endowment 12, 11 (2019), 1344–1356. https://doi.org/10.14778/3342263.3342272 Tashin Reza, Matei Ripeanu, Geoffrey Sanders, and Roger Pearce

    work page doi:10.14778/3342263.3342272 2019

  52. [52]

    In Proceedings of the 2020 ACM SIGMOD International Conference on Management of Proc

    Approximate pattern matching in massive graphs with precision and recall guarantees. In Proceedings of the 2020 ACM SIGMOD International Conference on Management of Proc. ACM Program. Lang., Vol. 10, No. OOPSLA1, Article

    2020

  53. [53]

    1115–1131

    Geo: A Query Rewrite Framework for Graph Pattern Mining 131:29 Data. 1115–1131. https://doi.org/10.1145/3318464.3380566 Rahmtin Rotabi, Krishna Kamath, Jon Kleinberg, and Aneesh Sharma

    work page doi:10.1145/3318464.3380566

  54. [54]

    In Proceedings of the 26th International Conference on World Wide Web Companion (Perth, Australia) (WWW ’17 Companion)

    Detecting Strong Ties Using Network Motifs. In Proceedings of the 26th International Conference on World Wide Web Companion (Perth, Australia) (WWW ’17 Companion). 983–992. https://doi.org/10.1145/3041021.3055139 Soumajyoti Sarkar, Ruocheng Guo, and Paulo Shakarian

    work page doi:10.1145/3041021.3055139

  55. [55]

    Using network motifs to characterize temporal network evolution leading to diffusion inhibition

    Using Network Motifs to Characterize Temporal Network Evolution Leading to Diffusion Inhibition. CoRR abs/1903.00862 (2019). arXiv:1903.00862 http://arxiv.org/abs/1903.00862 Yingxia Shao, Bin Cui, Lei Chen, Lin Ma, Junjie Yao, and Ning Xu

    work page internal anchor Pith review Pith/arXiv arXiv 1903

  56. [56]

    In Proceedings of the 2014 International Conference on Management of Data (Snowbird, UT, USA) (SIGMOD ’14)

    Parallel Subgraph Listing in a Large-Scale Graph. In Proceedings of the 2014 International Conference on Management of Data (Snowbird, UT, USA) (SIGMOD ’14). 625–636. https://doi.org/10.1145/2588555.2588557 Tianhui Shi, Mingshu Zhai, Yi Xu, and Jidong Zhai

    work page doi:10.1145/2588555.2588557 2014

  57. [57]

    InProceedings of the 2020 International Conference on Management of Data (Portland, OR, USA) (SIGMOD ’20)

    In-Memory Subgraph Matching: An In-Depth Study. InProceedings of the 2020 International Conference on Management of Data (Portland, OR, USA) (SIGMOD ’20). 1083–1098. https://doi.org/10.1145/3318464. 3380581 Brian K Tanner, Gary Warner, Henry Stern, and Scott Olechowski

    work page doi:10.1145/3318464 2020

  58. [58]

    In 2010 eCrime Researchers Summit

    Koobface: The evolution of the social botnet. In 2010 eCrime Researchers Summit . IEEE, 1–10. https://doi.org/10.1109/ecrime.2010.5706694 Li Wang, Hongying Zhao, Jing Li, Yingqi Xu, Yujia Lan, Wenkang Yin, Xiaoqin Liu, Lei Yu, Shihua Lin, Michael Yifei Du, Xia Li, Yun Xiao, and Yunpeng Zhang

    work page doi:10.1109/ecrime.2010.5706694 2010

  59. [59]

    Oncogene 39, 3 (Sept

    Identifying Functions and Prognostic Biomarkers of Network Motifs Marked By Diverse Chromatin States in Human Cell Lines. Oncogene 39, 3 (Sept. 2019), 677–689. https://doi.org/10.1038/s41388- 019-1005-1 Runji Wang

    work page doi:10.1038/s41388- 2019

  60. [60]

    Proceedings of the ACM on Management of Data 1, 2, Article 150 (June 2023), 23 pages

    Free Join: Unifying Worst-Case Optimal and Traditional Joins. Proceedings of the ACM on Management of Data 1, 2, Article 150 (June 2023), 23 pages. https://doi.org/10.1145/3589295 Zhaoguo Wang, Zhou Zhou, Yicun Yang, Haoran Ding, Gansen Hu, Ding Ding, Chuzhe Tang, Haibo Chen, and Jinyang Li

    work page doi:10.1145/3589295 2023

  61. [61]

    InProceedings of the 2022 International Conference on Management of Data (Philadelphia, PA, USA) (SIGMOD ’22)

    WeTune: Automatic Discovery and Verification of Query Rewrite Rules. InProceedings of the 2022 International Conference on Management of Data (Philadelphia, PA, USA) (SIGMOD ’22). Association for Computing Machinery, New York, NY, USA, 94–107. https://doi.org/10.1145/3514221.3526125 Daniel Weiss and Gary Warner

    work page doi:10.1145/3514221.3526125 2022

  62. [62]

    Tracking criminals on facebook: A case study from a digital forensics reu program. (2015). Max Willsey, Chandrakana Nandi, Yisu Remy Wang, Oliver Flatt, Zachary Tatlock, and Pavel Panchekha

    2015

  63. [63]

    egg: Fast and Extensible Equality Saturation. Proc. ACM Program. Lang. 5, POPL, Article 23 (Jan. 2021), 29 pages. https: //doi.org/10.1145/3434304 Ziniu Wu, Parimarjan Negi, Mohammad Alizadeh, Tim Kraska, and Samuel Madden

    work page doi:10.1145/3434304 2021

  64. [64]

    Proceedings of the ACM on Management of Data 1, 1, Article 41 (May 2023), 27 pages

    FactorJoin: A New Cardinality Estimation Framework for Join Queries. Proceedings of the ACM on Management of Data 1, 1, Article 41 (May 2023), 27 pages. https://doi.org/10.1145/3588721 Yichen Yang, Mangpo Phitchaya Phothilimtha, Yisu Remy Wang, Max Willsey, Sudip Roy, and Jacques Pienaar. 2021b. Equality Saturation for Tensor Graph Superoptimization. ArXi...

    work page doi:10.1145/3588721 2023

  65. [65]

    Geo: A Query Rewrite Framework for Graph Pattern Mining

    Artifact for "Geo: A Query Rewrite Framework for Graph Pattern Mining". https://doi.org/10.5281/zenodo.18503157 Hao Zhang, Jeffrey Xu Yu, Yikai Zhang, Kangfei Zhao, and Hong Cheng

    work page doi:10.5281/zenodo.18503157

  66. [66]

    Proceedings of the VLDB Endowment 13, 12 (July 2020), 2493–2507

    Distributed Subgraph Counting: A General Approach. Proceedings of the VLDB Endowment 13, 12 (July 2020), 2493–2507. https://doi.org/10.14778/3407790.3407840 Xuanhe Zhou, Guoliang Li, Chengliang Chai, and Jianhua Feng

    work page doi:10.14778/3407790.3407840 2020

  67. [67]

    A learned query rewrite system using Monte Carlo tree search. Proc. VLDB Endow. 15, 1 (Sept. 2021), 46–58. https://doi.org/10.14778/3485450.3485456 Philip Zucker and Andrés Goens

    work page doi:10.14778/3485450.3485456 2021

  68. [68]

    By induction on n

    131:34 Nazanin Yousefian, Kasra Jamshidi, Keval Vora, and Anders Miltner Proof. By induction on n. Case 1: 𝑛 = 0 𝑡 →∗ 𝑅∪𝑇 𝑡 Case 2: 𝑛 = 𝑛′ + 1 Let 𝜑 (𝑡) ≡ 𝐸 𝜑 (𝑡 ′). This means 𝜑 (𝑡) and 𝜑 (𝑡 ′) are represented by the same e-class 𝑒𝑐. We do not prove the soundness of e-graphs in this paper (existing result from Nelson and Oppen [Nelson and Oppen 1980]), s...

    1980

  69. [69]

    Publication date: April 2026

    2026