Superfluous Arcs and Confluent Reductions in the Minimum Feedback Vertex Set Problem
Bibliographic record
Abstract
Given a directed graph (digraph) G with vertex set V, a Feedback Vertex Set (FVS) is a subset of vertices whose removal eliminates all circuits in G. Finding a minimum feedback vertex set (MFVS) is NP-hard, but digraph reductions can reduce graph size while preserving at least one MFVS. This raises questions about the ordering in which reductions are applied and the existence of an optimal order that maximizes size reduction. The Church-Rosser property (confluence) ensures reductions can be applied in any order, leading to a unique reduced digraph up to isomorphism. In this work, we focus on arc reduction and its confluence within a broader set of known confluent reductions. We introduce Superfluous Arcs, which can be removed without affecting MFVS solutions, and propose a new parametrized reduction, chordk, to identify and remove specific superfluous arcs in polynomial time for bounded integer k. We establish the confluence of a set of reductions that includes chordk, creating the largest known confluent reduction system for MFVS, which improves preprocessing techniques for solving the MFVS problem efficiently.
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".