Bibliographic record
Abstract
Let G = (V, E) be an edge-weighted complete graph representing a network in which the edges represent potential links, and the vertices (centres) are partitioned into two classes – vital vertices, which represent the vital core of the network, and secondary vertices. We consider the vital core connectivity problem (VCC), which is the problem of finding a minimum weight spanning multi-subgraph of G which is k-edge connected overall and whose vital core remains at least l-edge connected even if some or all of the secondary vertices are removed. The VCC arises naturally in many practical applications in which one wishes to design a network at minimum cost which will not only survive the loss of a certain number of links overall, but for which the vital core remains at least l-edge connected even if some or all of the secondary centres are lost. We show that the VCC is, in general, NP-hard, and present the first constant factor approximation algorithm for this problem, as well as give an upper bound on the integrality gap of its linear programming relaxation. In particular, we show an approximation guarantee (and upper bound on the integrality gap) of 8 3 for l ≥ ⌈
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 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".