On the Parameterized Complexity of Deletion to \(\boldsymbol{\mathcal{H}}\)-Free Strong Components
Bibliographic record
Abstract
Abstract. Directed Feedback Vertex Set (DFVS) is a fundamental computational problem that has received a lot of attention in parameterized complexity. In this paper, we initiate the study of a wide generalization of this problem called the [Formula: see text]-free Strong Connected Component Deletion problem, where [Formula: see text] is a finite family of digraphs. Here, one is given a digraph [Formula: see text] and an integer [Formula: see text], and the objective is to decide whether there is a vertex set of size at most [Formula: see text] whose deletion results in a digraph where every strongly connected component excludes graphs in family [Formula: see text] as (not necessarily induced) subgraphs. When [Formula: see text] comprises only the digraph with a single arc, then this problem is precisely the DFVS problem. Our main result is a proof that this problem is fixed-parameter tractable parameterized by the size of the deletion set if [Formula: see text] only contains rooted graphs or if [Formula: see text] contains at least one directed path. Along with generalizing the fixed-parameter tractability result for DFVS, our result also generalizes the results of Göke, Marx, and Mnich [ Proceedings of the International Conference on Algorithms and Complexity, Springer, 2019, pp. 249–261] for the 1-Out-Regular Vertex Deletion and Bounded Size Strong Component Vertex Deletion problems. Moreover, we design algorithms for the two above-mentioned problems, whose running times are better and that match with the best bounds for DFVS, without using the heavy machinery of shadow removal as is done by Göke, Marx, and Mnich [ Proceedings of the International Conference on Algorithms and Complexity, Springer, 2019, pp. 249–261].
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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 | 0.003 | 0.030 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.003 | 0.005 |
| Scholarly communication | 0.010 | 0.021 |
| Open science | 0.006 | 0.007 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.030 | 0.003 |
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".