Improved Approximations for a CVRP with Unsplittable Demands
Bibliographic record
Abstract
In this paper, we present improved approximation algorithms for the (unsplittable) capacitated vehicle routing problem (CVRP) in general metrics. In the CVRP, we are given a set of points (clients) V together with a depot r in a metric space, with each [Formula: see text] having a demand [Formula: see text] and a vehicle of bounded capacity Q. The goal is to find a minimum cost collection of tours for the vehicle, each starting and ending at the depot, such that each client is visited at least once and the total demands of the clients in each tour are at most Q. In the unsplittable variant we study, the demand of a node must be served entirely by one tour. We present two approximation algorithms for the unsplittable CVRP: a combinatorial [Formula: see text]-approximation, where [Formula: see text] is the approximation factor for the traveling salesman problem, and an approximation algorithm based on linear programming rounding with approximation guarantee [Formula: see text] in [Formula: see text] time. Funding: This work was supported by the Canadian Network for Research and Innovation in Machining Technology and the Natural Sciences and Engineering Research Council of Canada. Z. Friggstad was supported by an NSERC Discovery Grant and a Discovery Grant Accelerator. M. R. Salavatipoura was supported by an NSERC Discovery Grant.
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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 | 0.016 |
| 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 | 0.001 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.006 | 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".