The Minimum Consistent Spanning Subset Problem on Trees
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Given a vertex-colored edge-weighted graph, the minimum consistent subset (MCS) problem asks for a minimum subset $S$ of vertices such that every vertex $v\notin S$ has the same color as its nearest neighbor in $S$. This problem is NP-complete. A recent result of Dey, Maheshwari, and Nandy (2021) gives a polynomial-time algorithm for the MCS problem on two-colored trees. A block is a maximal connected set of vertices of the same color. We introduce a variant of the MCS problem, namely the minimum consistent spanning subset problem, for which we require the set $S$ to contain a vertex from every block of the graph such that every vertex $v\notin S$ has a nearest neighbor in $S$ that is in the same block as $v$. We observe that this problem is NP-hard on general graphs. We present a polynomial-time algorithm for this problem on trees.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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