Evangelism in Social Networks: Algorithms and Complexity

TL;DR

This paper studies the complexity of selecting initial evangelists in social networks to maximize influence spread, providing algorithms for specific graph types and proving the problem's computational hardness.

Contribution

It introduces the influence maximization problem with a new threshold-based diffusion model, proves its computational hardness, and offers exact algorithms for trees and complete graphs.

Findings

The influence maximization problem is computationally hard to approximate.

Exact polynomial algorithms are provided for trees and complete graphs.

Parameterized algorithms are developed for general graphs.

Abstract

We consider a population of interconnected individuals that, with respect to a piece of information, at each time instant can be subdivided into three (time-dependent) categories: agnostics, influenced, and evangelists. A dynamical process of information diffusion evolves among the individuals of the population according to the following rules. Initially, all individuals are agnostic. Then, a set of people is chosen from the outside and convinced to start evangelizing, i.e., to start spreading the information. When a number of evangelists, greater than a given threshold, communicate with a node v, the node v becomes influenced, whereas, as soon as the individual v is contacted by a sufficiently much larger number of evangelists, it is itself converted into an evangelist and consequently it starts spreading the information. The question is: How to choose a bounded cardinality initial set of evangelists so as to maximize the final number of influenced individuals? We prove that the problem is hard to solve, even in an approximate sense. On the positive side, we present exact polynomial time algorithms for trees and complete graphs. For general graphs, we derive exact parameterized algorithms. We also investigate the problem when the objective is to select a minimum number of evangelists capable of influencing the whole network. Our motivations to study these problems come from the areas of Viral Marketing and the analysis of quantitative models of spreading of influence in social networks.