An Algorithm Based on Connectivity Properties for Finding Cycles and Paths on Kidney Exchange Compatibility Graphs
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Kidney-paired donation programs assist patients in need of a kidney to swap their incompatible donor with another incompatible patient–donor pair for a suitable kidney in return. The kidney exchange problem (KEP) is a mathematical optimization problem that consists of finding the maximum set of matches in a directed graph representing the pool of incompatible pairs. Depending on the specific framework, these matches can come in the form of (bounded) directed cycles or directed paths. This gives rise to a family of KEP models that have been studied over the past few years. Several of these models require an exponential number of constraints to eliminate cycles and chains that exceed a given length. In this paper, we present enhancements to a subset of existing models that exploit the connectivity properties of the underlying graphs, thereby rendering more compact and tractable models in both cycle-only and cycle-and-chain versions. In addition, an efficient algorithm is developed for detecting violated constraints and solving the problem. To assess the value of our enhanced models and algorithm, an extensive computational study was carried out comparing with existing formulations. The results demonstrated the effectiveness of the proposed approach. For example, among the main findings for edge-based cycle-only models, the proposed (*PRE(i)) model uses a new set of constraints and a small subset of the full set of length-k paths that are included in the edge formulation. The proposed model was observed to achieve a more than 98% reduction in the number of such paths among all tested instances. With respect to cycle-and-chain formulations, the proposed (*ReSPLIT) model outperformed Anderson’s arc-based (AA) formulation and the path constrained-TSP formulation on all instances that we tested. In particular, when tested on a difficult sets of instances from the literature, the proposed (*ReSPLIT) model provided the best results compared to the AA and PC-based models.
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.
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 | 0.000 |
| 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