Approximation Algorithm for the Balanced 2-correlation Clustering Problem on Well-Proportional Graphs

In this paper, we consider the balanced 2-correlation clustering problem on well-proportional graphs, which has applications in protein interaction networks, cross-lingual link detection, communication networks, among many others. Given a complete graph \(G=(V,E)\) with each edge \((u,v)\in E\) labeled by \(+\) or −, the goal is to partition the vertices into two clusters of equal size to minimize the number of positive edges whose endpoints lie in different clusters plus the number of negative edges whose endpoints lie in the same cluster. We provide a \((3,\max \{4(M+1),16\})\)-balanced approximation algorithm for the balanced 2-correlation clustering problem on M-proportional graphs. Namely, the cost of the vertex partition \(\{V_1, V_2\}\) returned by the algorithm is at most \(\max \{4(M+1),16\}\) times the optimum solution, and \(\min \{|V_1|,|V_2|\} \le 3\max \{|V_1|\), \( |V_2|\}\).