Efficient computation of feedback arc set at web-scale
Bibliographic record
Abstract
The minimum feedback arc set problem is an NP-hard problem on graphs that seeks a minimum set of arcs which, when removed from the graph, leave it acyclic. In this work, we investigate several approximations for computing a minimum feedback arc set with the goal of comparing the quality of the solutions and the running times. Our investigation is motivated by applications in Social Network Analysis such as misinformation removal and label propagation. We present careful algorithmic engineering for multiple algorithms to improve the scalability of each approach. In particular, two approaches we optimize (one greedy and one randomized) provide a nice balance between feedback arc set size and running time complexity. We experimentally compare the performance of a wide range of algorithms on a broad selection of large online networks including Twitter, LiveJournal, and the Clueweb12 dataset. The experiments reveal that our greedy and randomized implementations outperform the other approaches by simultaneously computing a feedback arc set of competitive size and scaling to web-scale graphs with billions of vertices and tens of billions of arcs. Finally, we extend the algorithms considered to the probabilistic case in which arcs are realized with some fixed probability and provide detailed experimental comparisons.
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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 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".