Balancing Speed and Coverage by Sequential Seeding in Complex Networks

Jarosław Jankowski,Piotr Bródka,Radosław Michalski,Tomasz Kajdanowicz,Boleslaw K Szymanski,Przemysław Kazienko

doi:10.1038/s41598-017-00937-8

Abstract

Information spreading in complex networks is often modeled as diffusing information with certain probability from nodes that possess it to their neighbors that do not. Information cascades are triggered when the activation of a set of initial nodes – seeds – results in diffusion to large number of nodes. Here, several novel approaches for seed initiation that replace the commonly used activation of all seeds at once with a sequence of initiation stages are introduced. Sequential strategies at later stages avoid seeding highly ranked nodes that are already activated by diffusion active between stages. The gain arises when a saved seed is allocated to a node difficult to reach via diffusion. Sequential seeding and a single stage approach are compared using various seed ranking methods and diffusion parameters on real complex networks. The experimental results indicate that, regardless of the seed ranking method used, sequential seeding strategies deliver better coverage than single stage seeding in about 90% of cases. Longer seeding sequences tend to activate more nodes but they also extend the duration of diffusion. Various variants of sequential seeding resolve the trade-off between the coverage and speed of diffusion differently.

Highlights

Influence maximization problem in complex networks was defined by Kempe[9]
Our results show that deploying the same number of seeds in stages as in at once approach yields larger spread, than achieved in a single stage seeding thanks to use of diffusion between stages
Sequential seeding strategies are considered here for an independent cascade model representing stochastic diffusion of information over the network initiated by seeds[9]

Summary

Introduction

Influence maximization problem in complex networks was defined by Kempe[9]. Analyses of various factors affecting the diffusion and social influence in complex networks include the efficiency of using different centrality measures for ranking influencers for selection[10], impact of homophily for successful seeding[11], and heterogeneous thresholds on congestion[12], finding the critical initiator fraction beyond which the cascade becomes global[13] or importance of different network features in predicting spread[14]. We found a broad conditions under which there exists a sequential seeding using the same node ranking method but achieving the higher average coverage than the single stage seeding does. This condition is that there is a seed in the single stage seeding that is reachable from other seeds with non-zero probability. In the second stage, the latter will initiate a new node in place of the already active reachable seed (and perhaps more nodes in the subsequent diffusion), making the overall average coverage of the sequential seeding larger than the single stage one

Methods

Results

Conclusion