Robust Correlation Clustering Problem with Locally Bounded Disagreements

Min-max disagreements are an important generalization of the correlation clustering problem (CorCP). It can be defined as follows. Given a marked complete graph $G=(V, E)$ , each edge in is by positive label “+” or negative “−” based on similarity connected vertices. The goal to find xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{C}$ vertices xmlns:xlink="http://www.w3.org/1999/xlink">$V$ so minimize number at vertex with most disagreements. Here, cut edges and non-cut produced . This paper considers two robust min-max disagreements: outliers penalties. parameter xmlns:xlink="http://www.w3.org/1999/xlink">$\delta\in(0,1/14)$ we first provide threshold-based iterative algorithm LP-rounding technique, which xmlns:xlink="http://www.w3.org/1999/xlink">$(1/\delta, 7/(1-14\delta))$ -bi-criteria approximation for both one-sided bipartite graphs. Next, verify that above achieve ratio 21 penalties when set xmlns:xlink="http://www.w3.org/1999/xlink">$\delta=1/21$