Efficient Approximation Algorithms for Several Positive Influence Dominating Set Problems in Social Networks

Identifying positive influence dominating set (PIDS) with the smallest cardinality can produce positive effect with the minimal cost on a social network. The purpose of this article is to propose new approximation algorithms for the minimum PIDS problem and its variants such as the minimum connected PIDS and the minimum PIDS of multiplex networks, with the aim of finding target sets with smaller cardinality. Through the design of novel submodular potential function, we theoretically prove that new approximation algorithms yield approximation ratios with same order compared with existing algorithms. We further demonstrate the performance of our algorithm by showcasing its efficacy on several real-world and publicly available instances of social networks, thereby providing additional evidence that our proposed algorithm can identify PIDS with smaller cardinality.