Bibliographic record
Abstract
In the Set Connectivity problem, we are given an n-node edge-weighted undirected graph and a collection of h set pairs (Si, Ti), where Si and Ti are subsets of nodes. The goal is to compute a min-cost subgraph H so that, for each set pair (Si, Ti), there exists at least one path in H between some node in Si and some node in Ti. In this paper, we initiate the study of the Survivable Set Connectivity problem (SSC), i.e., the generalization of Set Connectivity where we are additionally given an integer requirement ki ≥ 1 for each set pair (Si, Ti), and we want to find a min-cost subgraph H so that there are at least ki edge-disjoint paths in H between Si and Ti. We achieve the following main results: • We show that there is no poly-logarithmic approx-imation for SSC unless NP has a quasi-polynomial time algorithm. This result is based on a reduc-tion from the Minimum Label Cover problem, and the result holds even for the special case where Si = {r} for all i, i.e., for the high-connectivity variant of the classical Group Steiner Tree prob-lem. More precisely, we prove an approximability lower bound of 2log 1− n for SSC, for any constant > 0, which is almost polynomial on n. A techni-cal novelty of our proof is the first use of a padding scheme technique for an edge-connectivity problem on undirected graphs. (Prior to our results, the applications of this technique only pertain to ei-ther node-connectivity problems or problems on di-rected graphs). • We present a bicriteria approximation algorithm for SSC that computes a solution H of cost at most ∗This work was partially done while the first and third authors
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.
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 | 0.015 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.005 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.004 | 0.016 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.015 | 0.002 |
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".