Positive Influence Dominating Set in Online Social Networks

Abstract

Abstract. Online social network has developed significantly in recent years as a medium of communicating, sharing and disseminating information and spreading influence. Most of current research has been on understanding the property of online social network and utilizing it to spread information and ideas. In this paper, we explored the problem of how to utilize online social networks to help alleviate social problems in the physical world, for example, the drinking, smoking, and drug related problems. We proposed a Positive Influence Dominating Set (PIDS) selection algorithm and analyzed its effect on a real online social network data set through simulations. By comparing the size and the average positive degree of PIDS with those of a 1-dominating set, we found that by strategically choosing 26% more people into the PIDS to participate in the intervention program, the average positive degree increases by approximately 3.3 times. In terms of the application, this result implies that by moderately increasing the participation related cost, the probability of positive influencing the whole community through the intervention program is significantly higher. We also discovered that a power law graph has empirically larger dominating sets (both the PIDS and 1-dominating set) than a random graph does.

Matheuristics for Variants of the Dominating Set Problem

“…In other words, in social networks there is a tendency for the behavior of connected users to match. Wang et al (2009) introduced the Positive Influence Dominating Set (PIDS) problem and analyzed its effect on a real online social network data set through simulations. This problem is defined as follows: given a graph G = (V, E) and being d(i) the degree of vertex i, a PIDS is a subset D ∈ V such that any vertex i ∈ V is dominated by at least Many works have been published since Wang et al (2009).…”

On the approximability of positive influence dominating set in social networks

“…Thus, they are expected to capture the most influential people in networks. Since both problems are NP-hard [18], research efforts have been spent on studying approximability of the problems.…”

“…We achieve the explicit constant 1/2 in the approximation factor by adjusting the complex construction of the set cover problem [6]. This differs from previous approaches [3,18,21] in which hardness results of set cover and dominating set problems are used in a "blackbox fashion".…”

“…Influence propagation with a limited number of hops as well as a special case of TPIDS, when ρ = 1/2 were first considered in Wang et al [18] in which they iteratively add (normal) dominating sets until forming a TPIDS. Feng et al [19] showed NP-completeness for the PIDS problem, when ρ = 1/2.…”

Discovering Shared Interests in Online Social Networks

“…The benefits of online social networks have gone beyond connecting people with information, as many recent studies have exploited online social networks for a variety of important applications, including mitigating multiple identities attacks (also known as Sybil attacks) [27], improving online marketplaces [28], and spreading positive influence [29].…”