Conflict-Aware Weighted Bipartite B-Matching and Its Application to E-Commerce
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Bibliographic record
Abstract
The weighted bipartite b-matching problem (WBM) plays a significant role in many real-world applications, including resource allocation, scheduling, Internet advertising, and E-commerce. WBM has been widely studied and efficient matching algorithms are well known. In this work, we study a novel variant of WBM, called conflict-aware WBM (CA-WBM), where conflict constraints are present between vertices of the bipartite graph. In CA-WBM, if two vertices (on the same side) are in conflict, they may not be included in the matching result simultaneously. We present a generalized formulation of CA-WBM in the context of E-commerce, where diverse matching results are often desired (e.g., movies of different genres and merchants selling products of different categories). While WBM is efficiently solvable in polynomial-time, we show that CA-WBM is NP-hard. We propose approximate and randomized algorithms to solve CA-WBM and show that they achieve close to optimal solutions via comprehensive experiments using synthetic datasets. We derive a theoretical bound on the approximation ratio of a greedy algorithm for CA-WBM and show that it is scalable on a large-scale real-world dataset.
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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 | 0.000 | 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 | 0.001 |
| Open science | 0.000 | 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