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Partial Optimality and Fast Lower Bounds for Weighted Correlation Clustering
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add ICP dual re-weighting of input weights (lambda=1/2) before GAEC (ablation) | GAEC heuristic · Image Seg., Knott-3D, Epinions, Slashdot | gap to best known objective (%): e.g. Epinions 1.75% -> 0.56% | Helped |
| add ICP dual re-weighting before GAEC+KLj (KLj on original weights) (ablation) | GAEC+KLj heuristic · Image Seg., Knott-3D, Epinions, Slashdot | gap to best known objective (%): Epinions 0.18% -> 0.12%, Image Seg 0.34% -> 0.10%, Knott-3D-450 6.46s vs 8.71s runtime; Slashdot 6.69% -> 6.58% | Mixed |
| ICP lower bound instead of LP relaxation | lower bound computation · Epinions, Slashdot | runtime to convergence and bound quality: ICP converges under 10^2 s; MPC matches at ~10^3 s; ICP gap 8.60% vs MPC 7.54% on Epinions | Mixed |
| use ICP cycle packing instead of LP relaxation for lower bounds | small instances (Knott-3D-450) · Knott-3D-450 | lower bound gap (%) and time: ICP gap 0.18% vs LP 0.00%; ICP 3.31 s vs LP 2174.95 s | Mixed |
| add partial optimality reduction (dominant edges, single-node cut preprocessing) (ablation) | weighted correlation clustering instances · Epinions, Slashdot | runtime of GAEC+KLj: decreased by more than 70% | Helped |
| add partial optimality reduction (dominant edges, single-node cut preprocessing) | weighted correlation clustering instances · Knott-3D-450 and Image Seg. | fraction of edges remaining: Knott-3D-450 92.4% of edges remain; Image Seg. 62.7% | No clear effect |
| add dominant-repulsive-edge criteria beyond Alush & Goldberger conditions (ablation) | partial optimality · Image Seg. | non-persistent edges remaining (%): 62.7% (ours) vs 85.6% (Alush & Goldberger criteria only, E†) | Helped |
Closest papers by meaning
- Partial Optimality in Cubic Correlation Clustering (ICML 2023 · similarity 0.92)
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- Improved Approximation Algorithms for Chromatic and Pseudometric-Weighted Correlation Clustering (NeurIPS 2025 · similarity 0.90)
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