On the Min-Max 2-Cluster Editing Problem

In this paper, we study the problem Min-Max 2-Cluster Editing which asks for a modification of a given graph into two maximal cliques by inserting or deleting edges such that the maximum number k of the editing edges incident to any vertex is minimized. We show the NP-hardness of the problem and present a polynomial-time algorithm when k < n/4, in which n is number of vertices. In addition, we design a 2-approximation algorithm and a branching algorithm for finding an optimal solution. By experiments on random graphs, we show that the exact algorithm is much more efficient than a trivial one.