The spread of information about products, ideas, and behaviors, and their adoption, is an important tool in viral marketing and communication strategies in politics. Shi et al. assume that social networks play a unique role in this process, and they consider social networks as a group of individuals connected through nodes. As a paradigm of an individual’s social activities and beliefs, presented through the influence of known individuals, the authors try to extend the research on positive influence in social networks found in their previous work. They also assume that selected individuals could “positively influence other [individuals (nodes)] in a social network,” taking into account a greedy approximation algorithm for the positive influence dominating set.

Since time is a key factor in the positive influence within social networks, the authors include a time-bounded algorithm in their study. With brief insight into the literature and previous work on the influence maximization problem, the real task is to present its definition in the context of a time-bounded frame. Thus, they provide some basic definitions, including positive influence dominating sets (PIDS) and time-bounded PIDS (tPIDS). In the context of social network utilization in commercial and political cases, constructing a tPIDS is a way to find individuals who can positively influence an entire network within an expected amount of time. The authors also give a clear definition of their algorithm based on a t-SPREAD graph, where the goal is to find a minimum tPIDS that provides minimum cost to positively influence the given network in a certain timeframe.

The real value of the paper is in its presentation of experiments that were conducted in “real-world networks to evaluate the performance and efficiency of [the] moving-down algorithm and [its counterpart], the improved algorithm.” The research was on studying real-world impacts on time-bounded positive influence in social networks through an Erdos-Renyi network graph. The authors studied the impact of the number of nodes and of average degree (with 1000 and 5000 nodes respectively, making the graph of the relationship between network size and the spread times). In addition, they looked at the impact of node numbers on time efficiency for the greedy algorithm, including the average degree of the network impact on time efficiency compared to PIDS. The main distinction between this algorithm and tPIDS is clearly presented: PIDS aims to find a dominated set that will influence all nodes in the entire network and tPIDS aims “to find a dominating set to influence other individuals in a certain bounded time.”

Since time is the crucial factor in any successful social interaction, especially in positive influence, its inclusion in an algorithm is a novel approach in studying positive influence in social networks. The authors provide detailed descriptions of their model, which should interest those working in viral marketing and similar businesses, and could serve as a basis for further research.