This talk aims at describing two aspects, to tackle the well known Minimum Connectivity Inference (MCI) problem, which is an N Phard problem. The first idea focuses state of the art Constraint Generation Algorithm (CGA). In general, the CGA uses cutset formulation of the MCI problem in its successive iterations. However, the strength of multicut approach has been established in the literature. Therefore, the aspect of using multicut setup in iterative process of the CGA will be discussed. Secondly, the harder instances of the MCI problem will be reviewed. The factors effecting the hardness of such instances will be considered as well.