Dynamic Relaxations for Online Bipartite Matching
Bibliographic record
Abstract
Online bipartite matching (OBM) is a fundamental model underpinning many important applications, including search engine advertisement, website banner and pop-up ads, and ride hailing. We study the independent and identically distributed (i.i.d.) OBM problem, in which one side of the bipartition is fixed and known in advance, whereas nodes from the other side appear sequentially as i.i.d. realizations of an underlying distribution and must immediately be matched or discarded. We introduce dynamic relaxations of the set of achievable matching probabilities; show how they theoretically dominate lower dimensional, static relaxations from previous work; and perform a polyhedral study to theoretically examine the new relaxations’ strength. We also discuss how to derive heuristic policies from the relaxations’ dual prices in a similar fashion to dynamic resource prices used in network revenue management. We finally present a computational study to demonstrate the empirical quality of the new relaxations and policies. Summary of Contribution: Online bipartite matching (OBM) is one of the fundamental problems in the area of online decision analysis with a wide variety of applications in operations research and computer science, for example, online advertising, ride sharing, and general resource allocation. Over the last decades, both communities have been interested in the design and analysis of new approaches. Our main contribution is to provide a polyhedral study that considers the problem’s sequential nature. Specifically, we achieve this via dynamic relaxations. We also discuss how to derive heuristic policies from the relaxations’ dual prices. We support our theoretical findings with a detailed computational study.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.022 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.014 | 0.002 |
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".