Graph Partitioning with the Party Library: Helpful-Sets in Practice
Bibliographic record
Abstract
Graph partitioning is an important subproblem in many applications. To partition a graph into more than two parts, there exist two different commonly used approaches: Either the graph is partitioned directly into the desired amount of partitions or the graph is first split into two partitions that are then further divided recursively. It has been shown that even optimal recursive bisection can lead to solutions "very far from the optimal one". However, for "important graph classes" recursive bisection solutions are known to be "almost always" within a constant factor of the optimal one. Thus, the question arises how good recursive bisection performs in practice. In this paper we describe enhancements to the Party graph partitioning library which is based on the helpful-set bisection heuristic and present results of extensive tests undertaken with it. We thereby compare Party with the two state-of-the art libraries Metis and Jostle using a permutation based evaluation scheme. We show experimentally that there are indeed many cases where a recursive application of a good bisection heuristic is likely to find better solutions than up-to-date direct approaches.
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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 | 0.002 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.014 | 0.003 |
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".