The Bipartite Polarization Problem is an optimization problem where the goal is to find the highest polarized bipartition on a weighted and labelled graph that represents a debate developed through some social network, where nodes represent user's opinions and edges agreement or disagreement between users. This problem can be seen as a generalization of the maxcut problem, and in previous work approximate solutions and exact solutions have been obtained for real instances obtained from Reddit discussions, showing that such real instances seem to be very easy to solve. In this paper, we investigate further the complexity of this problem, by introducing an instance generation model where a single parameter controls the polarization of the instances in such a way that this correlates with the average complexity to solve those instances. The average complexity results we obtain are consistent with our hypothesis: the higher the polarization of the instance, the easier is to find the corresponding polarized bipartition.

翻译：二分极化问题是一个优化问题，目标是在一个表示通过社交网络展开的辩论的加权标记图上找到极化程度最高的二分划分，其中节点代表用户观点，边代表用户之间的赞同或反对关系。该问题可被视为最大割问题的一般化，在先前工作中，已针对从Reddit讨论中获取的真实实例获得了近似解和精确解，表明此类真实实例似乎非常容易求解。本文通过引入一个实例生成模型进一步研究了该问题的复杂性，该模型中单个参数控制实例的极化程度，使得该参数与求解这些实例的平均复杂性相关联。我们获得的平均复杂性结果与假设一致：实例的极化程度越高，就越容易找到相应的极化二分划分。