OrbitSI: An Orbit-based Algorithm for the Subgraph Isomorphism Search Problem
Bibliographic record
Abstract
The Subgraph Isomorphism (SI) search problem searches for embeddings of a pattern graph within a data graph. Efficient heuristic algorithms for the SI search problem are often structured around a Depth-First Search (DFS) tree-based search to find matching subgraphs. These algorithms comprise three segments: filtering, ordering and enumeration. Filtering and ordering are critical in reducing the runtime of the enumeration segment. As such, various properties of vertices are used to filter out impossible matches and determine the most efficient enumeration order. In this paper, we propose using the graphs’ local topological information to strengthen the filtering and ordering segments of a heuristic algorithm, going beyond the properties of vertices and their immediate neighbours, which make up the state-of-the-art strategies. We use orbit counts of 4-vertex graphlets to characterise the local topology near a vertex, which provides valuable structural information while keeping the computational effort for analysing the topology affordable. Our new algorithm, OrbitSI, improves the overall runtime across eight datasets, each containing one data graph and 1800 pattern graphs, by factors of 2.69 to 11.49 compared to four state-of-the-art algorithms.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.005 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.009 | 0.004 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".