Minimizing Polarization and Disagreement in Social Networks via Link Recommendation
Authors: Liwang Zhu, Qi Bao, Zhongzhi Zhang

Individual's opinions are fundamentally shaped  and evolved by their interactions with other people, and social phenomena such as disagreement and polarization are now tightly woven into daily life. The quantification and optimization of these concepts have been the subject of much recent research behind a wealth of high-impact data mining applications. In particular, researchers have addressed the question of how such concepts can be optimized by influencing the opinion of a small number of individuals or by designing the network from scratch.Here, rather than  a “design-from-scratch” approach or altering the initial opinion, we study the optimization problem of recommending $k$ new links to minimize the sum of polarization and disagreement in a social network with $n$ nodes and $m$ edges.  We show that our objective function of this combinatorial optimization problem is not submodular, although it is monotone. We propose a simple greedy algorithm with a constant-factor approximation that  solves the problem in cubic running time, and we provide  theoretical analysis of the approximation guarantee for the algorithm. To overcome the computation challenge for large networks, we also provide a fast algorithm with computation complexity $\Otil (mk\eps^{-2})$ for any $\eps>0$,  where the $\Otil (\cdot)$ notation suppresses the ${\rm poly} (\log n)$ factors. Extensive experiments on real datasets demonstrate both the efficiency and effectiveness of our algorithms.