A local search algorithm for the constrained max cut problem on hypergraphs.
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Bibliographic record
Abstract
In the constrained max k -cut problem on hypergraphs, we are given a weighted hypergraph H=(V, E) , an integer k and a set c of constraints. The goal is to divide the set V of vertices into k disjoint partitions in such a way that the sum of the weights of the hyperedges having at least two endpoints in different partitions is maximized and the partitions satisfy all the constraints in c . In this paper we present a local search algorithm for the constrained max k -cut problem on hypergraphs and show that it has approximation ratio 1-1/k for a variety of constraints c , such as for the constraints defining the max Steiner k -cut problem, the max multiway cut problem and the max k -cut problem. We also show that our local search algorithm can be used on the max k -cut problem with given sizes of parts and on the capacitated max k -cut problem, and has approximation ratio 1-|V max |/|V| , where |V max | is the cardinality of the biggest partition. In addition, we present a local search algorithm for the directed max k -cut problem that has approximation ratio (k-1)/(3k-2).
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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 | 0.000 |
| 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