Approximation Algorithm for Min-max Correlation Clustering Problem with Penalties.

This paper introduces the min-max correlation clustering problem with penalties, which is a generalization of the correlation clustering problem. In this problem, each vertex can be clustered or penalized, and the goal of the problem is to minimize the sum of the number of error edges and the penalty cost at the worst vertex. In this paper, we give an integer programming and linear programming relaxation of the problem, and provide a constant approximation algorithm of the problem based on LP-rounding technique.