Maximum Closeness Centrality <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>k</mml:mi></mml:math>-Clubs: A Study of Dock-Less Bike Sharing
Bibliographic record
Abstract
In this work, we investigate a new paradigm for dock-less bike sharing. Recently, it has become essential to accommodate connected and free-floating bicycles in modern bike-sharing operations. This change comes with an increase in the coordination cost, as bicycles are no longer checked in and out from bike-sharing stations that are fully equipped to handle the volume of requests; instead, bicycles can be checked in and out from virtually anywhere. In this paper, we propose a new framework for combining traditional bike stations with locations that can serve as free-floating bike-sharing stations. The framework we propose here focuses on identifying highly centralized k -clubs (i.e., connected subgraphs of restricted diameter). The restricted diameter reduces coordination costs as dock-less bicycles can only be found in specific locations. In addition, we use closeness centrality as this metric allows for quick access to dock-less bike sharing while, at the same time, optimizing the reach of service to bikers/customers. For the proposed problem, we first derive its computational complexity and show that it is NP -hard (by reduction from the 3-SATISFIABILITY problem), and then provide an integer programming formulation. Due to its computational complexity, the problem cannot be solved exactly in a large-scale setting, as is such of an urban area. Hence, we provide a greedy heuristic approach that is shown to run in reasonable computational time. We also provide the presentation and analysis of a case study in two cities of the state of North Dakota: Casselton and Fargo. Our work concludes with the cost-benefit analysis of both models (docked vs. dockless) to suggest the potential advantages of the proposed model.
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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 | 0.003 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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 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".