An efficient cost-sharing mechanism for the prize-collecting Steiner forest problem
Why this work is in the frame
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Bibliographic record
Abstract
In an instance of the prize-collecting Steiner forest problem (PCSF) we are given an undirected graph G = (V,E), non-negative edge-costs c(e) for all e ∈ E, terminal pairs R = {(si,ti)}1≤i≤k, and penalties π1,...,πk. A feasible solution (F,Q) consists of a forest F and a subset Q of terminal pairs such that for all (si,ti) ∈ R either si,ti are connected by F or (si,ti) ∈ Q. The objective is to compute a feasible solution of minimum cost c(F) + π(Q). A game-theoretic version of the above problem has k players, one for each terminal-pair in R. Player i’s ultimate goal is to connect si and ti, and the player derives a privately held utility ui ≥ 0 from being connected. A service provider can connect the terminals si and ti of player i in two ways: (1) by buying the edges of an si,ti-path in G, or (2) by buying an alternate connection between si and ti (maybe from some other provider) at a cost of πi. In this paper, we present a simple 3-budgetbalanced and group-strategyproof mechanism for the above problem. We also show that our mechanism computes client sets whose social cost is at most O(log 2 k) times the minimum social cost of any player set. This matches a lower-bound that was recently given by Roughgarden and Sundararajan (STOC ’06).
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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 | 0.005 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.006 |
| Science and technology studies | 0.005 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.006 | 0.003 |
| Research integrity | 0.000 | 0.002 |
| 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