Bibliographic record
Abstract
Given an undirected graph G and a subset of vertices S ⊆ V(G), we call the vertices in S the terminal vertices and the vertices in V (G) - S the Steiner vertices. In this thesis, we study two problems whose goals are to achieve high "connectivity" among the terminal vertices. The first problem is the STEINER TREE PACKING problem, where a Steiner tree is a tree that connects the terminal vertices (Steiner vertices are optional). The goal of this problem is to find a largest collection of edge-disjoint Steiner trees. The second problem is the STEINER ROOTED-ORIENTATION problem. In this problem, there is a root vertex r among the terminal vertices. The goal is to find an orientation of all the edges in G so that the Steiner rooted-connectivity is maximized in the resulting directed graph D. The main result of the STEINER TREE PACKING problem is the following approximate min-max relation: If S is 24k-edge-connected in G, then there are k edge-disjoint Steiner trees. This answers Kriesell's conjecture affirmatively up to a constant multiple. We also generalize the above result to the STEINER FOREST PACKING problem. The main result of the STEINER ROOTED-ORIENTATION problem is the following approximate min-max relation: If S is 2k-hyperedge-connected in a hypergraph H, then there is a Steiner rooted k-hyperarc-connected orientation of H. The above result is best possible in terms of the connectivity bound. We shall start this thesis by describing the relations of the problems that we study to the network multicasting problem, which is the starting point of this work.
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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 | 0.013 | 0.057 |
| Meta-epidemiology (narrow) | 0.005 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.004 |
| Bibliometrics | 0.005 | 0.008 |
| Science and technology studies | 0.003 | 0.006 |
| Scholarly communication | 0.006 | 0.023 |
| Open science | 0.007 | 0.007 |
| Research integrity | 0.004 | 0.013 |
| Insufficient payload (model declined to judge) | 0.013 | 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".