GPU Acceleration of Graph Matching, Clustering, and Partitioning
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Bibliographic record
Abstract
We consider sequential algorithms for hypergraph partitioning and GPU (i.e., fine-grained shared-memory parallel) algorithms for graph partitioning and clustering. Our investigation into sequential hypergraph partitioning is concerned with the efficient construction of high-quality matchings for hypergraph coarsening and optimisation with respect to general hypergraph partitioning quality metrics. We introduce the l*(l-1)-metric which exactly measures the communication volume for a finite element computation, and show how to use an ordinary hypergraph bipartitioner to greedily optimise a partitioning with respect to a general quality metric. Graph partitioning and clustering on the GPU is achieved by implementing all parts of the multi-level paradigm (i.e., matching, coarsening, and refinement) on the GPU. We first develop GPU algorithms for matching and coarsening. These are then used as building blocks for a greedy agglomerative modularity clustering heuristic, with which we participated in the 10th DIMACS partitioning and clustering challenge. By combining the parallel matching and coarsening algorithms with a parallel partitioning refinement method and implementing these algorithms using general sparse matrix-vector multiplication operations, we are able to perform graph partitioning entirely on the GPU. The GPU partitioning algorithm is compared both in terms of quality and speed to the sequential METIS graph partitioner and is faster for graphs with a million or more vertices, while offering similar quality. The highest achieved speedup over METIS is 6.2, for which a graph with 24 million vertices and 29 million edges is partitioned into two parts in 3.7 seconds on the GPU (an NVIDIA Tesla C2075) with an edge cut of 329. This shows that the GPU can effectively be used for the multi-level analysis of large graphs.
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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 | 0.001 | 0.001 |
| 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