scholarly journals Adaptive Greedy versus Non-Adaptive Greedy for Influence Maximization

2020 ◽  
Vol 34 (01) ◽  
pp. 590-597 ◽  
Author(s):  
Wei Chen ◽  
Binghui Peng ◽  
Grant Schoenebeck ◽  
Biaoshuai Tao
Keyword(s):  
Greedy Algorithm ◽  
Threshold Model ◽  
Influence Maximization ◽  
Cascade Model ◽  
Maximization Problem ◽  
Expected Number ◽  
Feedback Model ◽  
Linear Threshold ◽  
Independent Cascade Model ◽  
Independent Cascade

We consider the adaptive influence maximization problem: given a network and a budget k, iteratively select k seeds in the network to maximize the expected number of adopters. In the full-adoption feedback model, after selecting each seed, the seed-picker observes all the resulting adoptions. In the myopic feedback model, the seed-picker only observes whether each neighbor of the chosen seed adopts. Motivated by the extreme success of greedy-based algorithms/heuristics for influence maximization, we propose the concept of greedy adaptivity gap, which compares the performance of the adaptive greedy algorithm to its non-adaptive counterpart. Our first result shows that, for submodular influence maximization, the adaptive greedy algorithm can perform up to a (1-1/e)-fraction worse than the non-adaptive greedy algorithm, and that this ratio is tight. More specifically, on one side we provide examples where the performance of the adaptive greedy algorithm is only a (1-1/e) fraction of the performance of the non-adaptive greedy algorithm in four settings: for both feedback models and both the independent cascade model and the linear threshold model. On the other side, we prove that in any submodular cascade, the adaptive greedy algorithm always outputs a (1-1/e)-approximation to the expected number of adoptions in the optimal non-adaptive seed choice. Our second result shows that, for the general submodular cascade model with full-adoption feedback, the adaptive greedy algorithm can outperform the non-adaptive greedy algorithm by an unbounded factor. Finally, we propose a risk-free variant of the adaptive greedy algorithm that always performs no worse than the non-adaptive greedy algorithm.

scholarly journals Multi-Winner Election Control via Social Influence: Hardness and Algorithms for Restricted Cases

Algorithms ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 251
Author(s):  
Mohammad Abouei Mehrizi ◽  
Gianlorenzo D'Angelo
Keyword(s):  
Social Influence ◽  
Threshold Model ◽  
Dynamic Programming Algorithm ◽  
Political Campaigns ◽  
Programming Algorithm ◽  
Linear Threshold ◽  
Independent Cascade Model ◽  
Voting System ◽  
Independent Cascade ◽  
Party Voting

Nowadays, many political campaigns are using social influence in order to convince voters to support/oppose a specific candidate/party. In election control via social influence problem, an attacker tries to find a set of limited influencers to start disseminating a political message in a social network of voters. A voter will change his opinion when he receives and accepts the message. In constructive case, the goal is to maximize the number of votes/winners of a target candidate/party, while in destructive case, the attacker tries to minimize them. Recent works considered the problem in different models and presented some hardness and approximation results. In this work, we consider multi-winner election control through social influence on different graph structures and diffusion models, and our goal is to maximize/minimize the number of winners in our target party. We show that the problem is hard to approximate when voters’ connections form a graph, and the diffusion model is the linear threshold model. We also prove the same result considering an arborescence under independent cascade model. Moreover, we present a dynamic programming algorithm for the cases that the voting system is a variation of straight-party voting, and voters form a tree.

Influence maximization on signed networks under independent cascade model

2018 ◽  
Vol 49 (3) ◽  
pp. 912-928 ◽  
Author(s):  
Wei Liu ◽  
Xin Chen ◽  
Byeungwoo Jeon ◽  
Ling Chen ◽  
Bolun Chen
Keyword(s):  
Influence Maximization ◽  
Cascade Model ◽  
Signed Networks ◽  
Independent Cascade Model ◽  
Independent Cascade

Positive influence maximization in signed social networks under independent cascade model

2020 ◽  
Vol 24 (19) ◽  
pp. 14287-14303 ◽  
Author(s):  
Jun Sheng ◽  
Ling Chen ◽  
Yixin Chen ◽  
Bin Li ◽  
Wei Liu
Keyword(s):  
Social Networks ◽  
Positive Influence ◽  
Influence Maximization ◽  
Cascade Model ◽  
Independent Cascade Model ◽  
Signed Social Networks ◽  
Independent Cascade

scholarly journals Balancing Spreads of Influence in a Social Network

2020 ◽  
Vol 34 (01) ◽  
pp. 3-10 ◽  
Author(s):  
Ruben Becker ◽  
Federico Corò ◽  
Gianlorenzo D'Angelo ◽  
Hugo Gilbert
Keyword(s):  
Social Media ◽  
Optimization Problem ◽  
General Setting ◽  
Natural Generalization ◽  
Constant Factor ◽  
Cascade Model ◽  
Expected Number ◽  
Exponential Time ◽  
Independent Cascade Model ◽  
Independent Cascade

The personalization of our news consumption on social media has a tendency to reinforce our pre-existing beliefs instead of balancing our opinions. To tackle this issue, Garimella et al. (NIPS'17) modeled the spread of these viewpoints, also called campaigns, using the independent cascade model introduced by Kempe, Kleinberg and Tardos (KDD'03) and studied an optimization problem that aims to balance information exposure when two opposing campaigns propagate in a network. This paper investigates a natural generalization of this optimization problem in which μ different campaigns propagate in the network and we aim to maximize the expected number of nodes that are reached by at least ν or none of the campaigns, where μ ≥ ν ≥ 2. Following Garimella et al., despite this general setting, we also investigate a simplified one, in which campaigns propagate in a correlated manner. While for the simplified setting, we show that the problem can be approximated within a constant factor for any constant μ and ν, for the general setting, we give reductions leading to several approximation hardness results when ν ≥ 3. For instance, assuming the gap exponential time hypothesis to hold, we obtain that the problem cannot be approximated within a factor of n−g(n) for any g(n) = o(1) where n is the number of nodes in the network. We complement our hardness results with an Ω(n−1/2)-approximation algorithm for the general setting when ν = 3 and μ is arbitrary.

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