A new diffusion-based multilevel algorithm for computing graph partitions of very high quality
Bibliographic record
Abstract
Graph partitioning requires the division of a graph's vertex set into k equally sized subsets such that some objective function is optimized. For many important ob jective functions, e. g., the number of edges incident to different partitions, the problem is MV-hard. Graph partitioning is an important task in many applications, so that a variety of algorithms and tools for its solution have been developed. Most state-of-the-art graph partitioning libraries use a variant of the Kernighan-Lin (KL) heuristic within a multilevel framework. While these libraries are very fast, their solutions do not always meet all requirements of the users. This includes the choice of the appropriate objective function and the shape of the computed partitions. Moreover, due to its sequential nature, the KL heuristic is not easy to parallelize. Thus, its use as a load balancer in parallel numerical applications requires complicated adaptations. That is why we have developed previously an inherently parallel algorithm, called BUBBLE-FOS/C (Meyerhenke et ah, IPDPS'06), which optimizes the partition shapes by a diffusive mechanism. Yet, it is too slow to be of real practical use, despite its high solution quality. In this paper, besides proving that BUBBLE-FOS/C converges towards a local optimum, we develop a much faster method for the improvement of partitionings. It is based on a different diffusive process, which is restricted to local areas of the graph and also contains a high degree of parallelism. By coupling this new technique with BUBBLE-FOS/C in a multilevel framework based on two different hierarchy construction methods, we obtain our new graph partitioning heuristic DibaP. Compared to BUBBLE-FOS/C, it shows a considerable acceleration, while retaining the positive properties of the slower algorithm. Experiments with popular benchmark graphs show an extremely good behavior. First, DibaP computes consistently better results - measured by the edge-cut and the number of boundary vertices in the summation and the maximum norm - than the state-of-the-art libraries METIS and JOSTLE. Second, with our new algorithm, we have improved the best known edge-cut values for a significant number of partitionings of six widely used benchmark graphs.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".