Chromatic correlation clustering incurs an additional chromatic penalty Delta(L) = ((L-1)/L)*0.0734 on top of the standard CC gap for color-independent methods, but the color-coupled C4 algorithm achieves the optimal 2.06 approximation.
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Why Colors Make Clustering Harder:Global Integrality Gaps, the Price of Fairness, and Color-Coupled Algorithms in Chromatic Correlation Clustering
Chromatic correlation clustering incurs an additional chromatic penalty Delta(L) = ((L-1)/L)*0.0734 on top of the standard CC gap for color-independent methods, but the color-coupled C4 algorithm achieves the optimal 2.06 approximation.