A group-strategyproof mechanism for Steiner forests
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Bibliographic record
Abstract
In this paper we design an approximately budget-balanced and group-strategyproof cost-sharing mechanism for the Steiner forest game. An instance of this game consists of an undirected graph G = (V, E), nonnegative costs ce for all edges e ∈ E, and a set R ⊆ V ×V of k terminal pairs. Each terminal pair (s, t) ∈ R is associated with an agent that wishes to establish a connection between nodes s and t in the underlying network. A feasible solution is a forest F that contains an s, t-path for each connection request (s, t) ∈ R. Previously, Jain and Vazirani [4] gave a 2approximate budget-balanced and group-strategyproof cost-sharing mechanism for the Steiner tree game — a special case of the game considered here. Such a result for Steiner forest games has proved to be elusive so far, in stark contrast to the well known primal-dual (2−1/k)-approximate algorithms [1, 2] for the problem. The cost-sharing method presented in this paper is 2-approximate budget-balanced and this is tight with respect to the budget-balance factor. Our algorithm is an original extension of known primal-dual methods for Steiner forests [1]. An interesting byproduct of the work in this paper is that our Steiner forest algorithm is (2−1/k)-approximate despite the fact that the forest computed by our method is usually costlier than those computed by known primal-dual algorithms. In fact the dual solution computed by our algorithm is infeasible but we can still prove that its total value is at most the cost of a minimum-cost Steiner forest for the given instance.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it