Sharing the cost more efficiently: improved approximation for multicommodity rent-or-buy
Why this work is in the frame
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Bibliographic record
Abstract
In the multicommodity rent-or-buy (MROB) network design problem we are given a network together with a set of k terminal pairs (s1, t1),..., (sk, tk). The goal is to provision the network so that a given amount of flow can be shipped between si and ti for all 1 ≤ i ≤ k simultaneously. In order to provision the network one can either rent capacity on edges at some cost per unit of flow, or buy them at some larger fixed cost. Bought edges have no incremental, flow-dependent cost. The overall objective is to minimize the total provisioning cost. Recently, Gupta et al. [7] presented a 12-approximation for the MROB problem. Their algorithm chooses a subset of the terminal pairs in the graph at random and then buys the edges of an approximate Steiner forest for these pairs. This technique has previously been introduced [8] for the single sink rent-or-buy network design problem. In this paper we give a 6.828-approximation for the MROB problem by refining the algorithm of Gupta et al. and simplifying their analysis. The improvement in our paper is based on a more careful adaptation and simplified analysis of the primal-dual algorithm for the Steiner forest problem due to Agrawal, Klein and Ravi [1]. Our result significantly reduces the gap between the single-sink [8] and multi-sink case.
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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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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