Polarization reduction by minimum‐cardinality edge additions: Complexity and integer programming approaches

Abstract

Real-world networks are often extremely polarized because the communication between different groups of vertices can be weak and, most of the time, only vertices within the same group or sharing the same beliefs communicate to each other. In this work, we introduce the minimum-cardinality edge addition problem (MinCEAP) as a strategy for reducing polarization in real-world networks based on a principle of minimum external interventions. We present the problem formulation and discuss its complexity, showing that its decision version is NP-complete. We also propose three integer programming formulations for the problem and discuss computational results on artificially generated and real-life instances. Randomly generated instances with up to 1000 vertices are solved to optimality. On the real-life instances, we show that polarization can be reduced to the desired threshold with the addition of a few edges. The minimum intervention principle and the methods developed in this work are shown to constitute an effective strategy for tackling polarization issues in practice in social, interaction, and communication networks, which is a relevant problem in a world characterized by extreme political and ideological polarization.

Network polarization, filter bubbles, and echo chambers: an annotated review of measures and reduction methods

“…The problem was shown to be NP‐hard. Preliminary results obtained by an iterated greedy heuristic were presented in Interian and Ribeiro (2019), while three integer programming formulations were compared in Interian et al. (2021) with computational results for both randomly generated and real‐life instances.…”

Network polarization, filter bubbles, and echo chambers: An annotated review of measures, models, and case studies

“…The second research question targeted network polarization reduction methods suggested in the literature, which are now exposed in this section. All of them have in common some attempt of changing different features of the network: add or remove edges [53,72]; introduce specific types of nodes (zealots [111], informed agents [59]); or the spread of random information [27]. The publications may propose methods to compute optimal interventions or analyze the impact of such modifications in the network structure, evaluating their effect on the polarization of the entire network or on the polarity of specific nodes.…”

“…Interian et al [71,72] proposed the minimum intervention principle, which assumes that the smallest number of changes should be made in the original network by any polarization reduction method. The issue of the insufficient communication between the polarized groups is solved by edge additions.…”

“…The problem was shown to be NP-hard. Preliminary results obtained by an iterated greedy heuristic were presented in [74], while three integer programming formulations were compared in [72] with computational results for both randomly generated and real-life instances. It was shown that the polarization could be reduced to the desired threshold by the addition of few edges, as established by the minimum intervention principle that guided the problem formulation.…”

“…Articles about different topics on the general subject of polarization appear in journals from different areas of knowledge, such as computer science [51,72], economics [28,77], or social and political sciences [45,87], authored by people who often do not communicate with each other. Researchers refer to phenomena related to polarization using different terms such as controversy [51], disagreement [19], conflict [107], and even cyberbalkanization [15], in addition to polarization itself.…”