Heuristic-Guided Iterative Compression for Efficient Graph Bipartization
Bibliographic record
Abstract
The Odd Cycle Transversal (OCT) problem, also known as Graph Bipartization, asks whether a given undirected graph can be made bipartite by deleting at most k vertices. Here, an odd cycle transversal means a subset of nodes with each appearing on one or more than one cycle. Although iterative compression algorithms are widely used for solving OCT within fixed-parameter tractable (FPT) bounds, their practical performance is often limited by the exponential number of subsets explored during compression. This paper introduces a heuristic-guided enhancement to iterative compression that integrates structural graph measures–such as degree, betweenness, and closeness centrality–to prioritize promising subsets and prune infeasible configurations early. The proposed method also reuses partial flows and colorings to reduce redundant computations. Experimental results demonstrate substantial runtime improvements, achieving 2x−4x speedups on synthetic and real-world graphs without sacrificing solution quality. Beyond empirical validation, we provide a formal analysis of the heuristic search space and discuss conditions under which compression complexity is reduced. These findings highlight the potential of structure-aware optimizations for scalable OCT solving in large graphs. In particular, such optimizations are relevant for applications in network reliability, communication systems, and large-scale graph analysis.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".