On non-progressive spread of influence through social networks

Abstract

Abstract. The spread of influence in social networks is studied in two main categories: the progressive model and the non-progressive model (see e.g. the seminal work of Kempe, Kleinberg, and Tardos in KDD 2003). While the progressive models are suitable for modeling the spread of influence in monopolistic settings, non-progressive are more appropriate for modeling non-monopolistic settings, e.g., modeling diffusion of two competing technologies over a social network. Despite the extensive work on the progressive model, non-progressive models have not been studied well. In this paper, we study the spread of influence in the nonprogressive model under the strict majority threshold: given a graph G with a set of initially infected nodes, each node gets infected at time τ iff a majority of its neighbors are infected at time τ − 1. Our goal in the MinPTS problem is to find a minimum-cardinality initial set of infected nodes that would eventually converge to a steady state where all nodes of G are infected. We prove that while the MinPTS is NP-hard for a restricted family of graphs, it admits an improved constant-factor approximation algorithm for power-law graphs. We do so by proving lower and upper bounds in terms of the minimum and maximum degree of nodes in the graph. The upper bound is achieved in turn by applying a natural greedy algorithm. Our experimental evaluation of the greedy algorithm also shows its superior performance compared to other algorithms for a set of realworld graphs as well as the random power-law graphs. Finally, we study the convergence properties of these algorithms and show that the nonprogressive model converges in at most O(|E(G)|) steps.

Active learning for networked data based on non-progressive diffusion model

“…Now we introduce the tools for proofs in this section. The proofs of lemma 2 and lemma 3 could be found in [8]. It is trivial to show that Minimum Source Set problem is NP-hard.…”

“…Progressive diffusion models have been extensively studied in the literature [25,4,11,3,26]. Fazli et al [8] proposed a greedy algorithm for non-progressive model and proved approximation ratio on power law graph. However, their works cannot be directly applied to active learning problem for the network data.…”

“…To model the correlation between labels of linked samples, we consider the probabilistic graphical model. In the setting of graphical model, we connect the active learning problem to the theory of non-progressive diffusion [8], and develop an instantiation model for the above problem. The active learning problem based on non-progressive diffusion is proved to be NP-hard.…”

Minimum Target Sets in Non-Progressive Threshold Models: When Timing Matters

“…This has catalyzed a growing interest in the quantitative analysis of opinion diffusion and collective decision-making mechanisms, cf. [24,20,15]. From a theoretical standpoint, it is pertinent to introduce and investigate mathematical models of influence diffusion, which simulate the process of how individuals revise their opinions and how the influence disseminates through social interactions.…”

“…One category of models which has gained significant popularity is the class of threshold models, cf. [36,24,1]. These models entail that each node v possesses a distinct threshold value τ (v) and updates its opinion to a positive state only when the number of its positive neighbors exceeds the stipulated threshold.…”