FASTiso: Fast Algorithm on Search state Tree for subgraph ISOmorphism in graphs of any size and density
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Bibliographic record
Abstract
Abstract Subgraph isomorphism is a fundamental combinatorial problem that involves finding one or more occurrences of a pattern graph within a target graph. It arises in a wide range of application domains, including biology, chemistry, social network analysis, and pattern recognition. Although subgraph isomorphism is NP-complete in the general case, many exact algorithms allow it to be solved in practice on many instances. However, the increasing size and structural diversity of graph datasets continue to pose significant challenges in terms of robustness and scalability. In this article, we propose FASTiso, an exact subgraph isomorphism algorithm that emphasizes a strong consistency between the variable ordering strategy and the pruning rules used during search. This design enables a unified exploitation of structural information throughout the exploration process, leading to improved efficiency and stable performance across heterogeneous graph structures. An extensive experimental evaluation on widely used synthetic and real-world benchmarks shows that FASTiso consistently outperforms reference solvers such as VF3, VF3L, and RI, and achieves competitive performance compared to constraint programming–based approaches (Glasgow, PathLad+), while outperforming them on most datasets. The results further demonstrate that FASTiso remains highly efficient on small instances and scales well to large graphs, while maintaining a lower memory footprint than most evaluated solvers. The peak memory usage is 7.74 GB for FASTiso, 36.19 GB for PathLad+, over 500 GB for Glasgow, 9.62 GB for VF3/VF3L, and 4.31 GB for RI. FASTiso code is available at https://gitlab.info.uqam.ca/cbe/fastiso as a C++ implementation, a Python module, and an integration within an extended version of NetworkX. The implementations support simple graphs and multigraphs, directed or undirected, with labels on nodes, edges, or both.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it