Efficient enumeration of the optimal solutions to the correlation clustering problem

According to the structural balance theory, a signed graph is considered structurally balanced when it can be partitioned into number of modules such that positive and negative edges are respectively located inside between modules. In practice, real-world networks rarely balanced, though. this case, one may want measure magnitude their imbalance, identify set causing imbalance. The correlation clustering (CC) problem precisely consists in looking for partition having least Recently, has been shown space optimal solutions CC constituted numerous diverse solutions. Yet, difficult explore, as NP-hard, exact approaches do not scale well even single solution. To alleviate issue, work we propose an efficient enumeration method allowing retrieve complete problem. It combines exhaustive strategy with neighborhoods varying sizes, achieve computational effectiveness. Results obtained middle-sized confirm usefulness our method.