The paper introduces a novel combinatorial algorithm for correlation clustering on unweighted complete graphs. It addresses the challenge of optimizing various norms of the disagreement vector simultaneously. The main focus is on minimizing disagreements while clustering similar vertices together and separating dissimilar ones. The authors propose an efficient algorithm that achieves Op1q-approximation for all ℓp-norm objectives, with improved run-time complexities based on graph properties. The study highlights the significance of balancing fairness and average welfare in clustering solutions, offering insights into universal algorithms and all-norms objectives across different optimization problems.
The research builds upon previous approximation algorithms for correlation clustering, emphasizing the importance of developing fast combinatorial approaches. By introducing the concept of adjusted correlation metrics, the authors demonstrate how to achieve constant-factor approximations for various ℓp-norm objectives efficiently. The results provide a significant advancement in understanding trade-offs between optimizing different norms and offer new perspectives on universal algorithms in combinatorial optimization problems.
To Another Language
from source content
arxiv.org
Principais Insights Extraídos De
by Sami Davies,... às arxiv.org 03-12-2024
https://arxiv.org/pdf/2308.01534.pdfPerguntas Mais Profundas