On positive influence dominating sets in social networks

Abstract

a b s t r a c tIn this paper, we investigate the positive influence dominating set (PIDS) which has applications in social networks. We prove that PIDS is APX-hard and propose a greedy algorithm with an approximation ratio of H(δ) where H is the harmonic function and δ is the maximum vertex degree of the graph representing a social network.

A cloud resource management model for the creation and orchestration of social communities

“…To confirm this observation the same experiment was re-run and node-degree distribution of the graphs were observed, shown in Figure 14. It was found that the Ss graphs are by nature scale free and conform to the power law distribution, which is consistent with previous research into graphical representations of social networks [43]. The reason for this distribution pattern lies in the generation algorithm which is developed such that 'association' nodes, representing the association (owner-owned) between CEs are dominant as every CE is owned by a parent CE, similarly, abstraction bonds become prominent within a CPT column however as the CPT grows and further types of bonds are added to the graph the new additions are CE specific such as temporal bonds, interface bonds and therefore do not occur in clusters.…”

Positive influence dominating sets in power-law graphs

“…They focus on finding a subset of a pre-established size that maximize the spread of information, but not the subset regardless of size that infuses information to the whole group. Wang et al (2009Wang et al ( , 2011 are the two papers most closely to this paper. Wang et al (2009) is the first one proposing the positive influence dominating set problem under the context of college drinking problem.…”

“…Wang et al (2009) proposed a dominating set augment based algorithm to construct PIDS from a given network. Wang et al (2011) proved the difficulty of PIDS problem in random graph and proposed a greedy algorithm with an approximation ratio of H(d) where H is the harmonic function and d is the maximum vertex degree of the graph representing a social network.…”

Matheuristics for Variants of the Dominating Set Problem

“…For example, a greedy algorithm with an approximation ratio of the n-th harmonic number. was proposed in Wang et al (2011). Dinh et al (2012) showed an approximation for this problem and Kim et al (2013) proposed an approach to identify effective leader groups of social networks based on the DS problem.…”