An efficient cost-sharing mechanism for the prize-collecting Steiner forest problem
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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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 | 0.004 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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 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".