Efficient Distance-Aware Influence Maximization in Geo-Social Networks

Abstract

Given a social network $\mathcal {G}$ and a positive integer $k$ , the influence maximization problem aims to identify a set of $k$ nodes in $\mathcal {G}$ that can maximize the influence spread under a certain propagation model. As the proliferation of geo-social networks, location-aware promotion is becoming more necessary in real applications. In this paper, we study the distance-aware influence maximization (DAIM) problem, which advocates the importance of the distance between users and the promoted location. Unlike the traditional influence maximization problem, DAIM treats users differently based on their distances from the promoted location. In this situation, the $k$ nodes selected are different when the promoted location varies. In order to handle the large number of queries and meet the online requirement, we develop two novel index-based approaches, MIA-DA and RIS-DA, by utilizing the information over some pre-sampled query locations. MIA-DA is a heuristic method which adopts the maximum influence arborescence (MIA) model to approximate the influence calculation. In addition, different pruning strategies as well as a priority-based algorithm are proposed to significantly reduce the searching space. To improve the effectiveness, in RIS-DA, we extend the reverse influence sampling (RIS) model and come up with an unbiased estimator for the DAIM problem. Through carefully analyzing the sample size needed for indexing, RIS-DA is able to return a $1 - 1/e -\epsilon$ approximate solution with at least $1 - \delta$ probability for any given query. Finally, we demonstrate the efficiency and effectiveness of proposed methods over real geo-social networks.