Crowd psychology plays an important role in determining the kind of activities that a person performs. In reality in a social network, crowd influence has been observed and it cannot be ignored when considering information diffusion problems. In this paper, we model crowd influence as a hyperedge $e=(H_e,\;v)$ with weight $0\leq P_e\leq 1$ , where $H_e$ is the head node set and $v$ is the tail node, means $v$ will be activated by $H_e$ with probability $P_e$ only after each node in $H_e$ is activated. Then, the Social Influence Maximization Problem in Hypergraph (SIMPH) aims to select $k$ initially-influenced seed users in a directed hypergraph $G=(V,\;E,\;P)$ . The objective is to maximize the expected number of eventually-influenced users. We show that SIMPH is NP-hard and the objective function is neither submodular nor supermodular. We develop a lower bound and an upper bound that are submodular. We prove maximizing these two bounds are NP-hard under IC model. Then we present a D-SSA algorithm for general weighted social influence maximization problem preserving ( $1-1/e-\in$ )-approximation. We formulate a sandwich approximation framework, which preserves a theoretical analysis result. Finally, we evaluate our algorithm on real world data sets. The results show the effectiveness and the efficiency of the proposed algorithm

Aiming at selecting a small subset of nodes with maximum influence on networks, the influence maximization (IM) problem has been extensively studied. Since it is #P-hard to compute the influence spread given a seed set, the state-of-the-art methods, including heuristic and approximation algorithms, are faced with great difficulties such as theoretical guarantee, time efficiency, generalization, and so on. This makes it unable to adapt to large-scale networks and more complex applications. On the other side, with the latest achievements of deep reinforcement learning (DRL) in artificial intelligence and other fields, lots of work have been focused on exploiting DRL to solve combinatorial optimization (CO) problems. Inspired by this, we propose a novel end-to-end DRL framework, ToupleGDD, to address the IM problem in this article, which incorporates three coupled graph neural networks (GNNs) for network embedding and double deep $Q$ -networks (DQNs) for parameters learning. Previous efforts to solve the IM problem with DRL trained their models on subgraphs of the whole network and then tested them on the whole graph, which makes the performance of their models unstable among different networks. However, our model is trained on several small randomly generated graphs with a small budget and tested on completely different networks under various large budgets, which can obtain results very close to IMM and better results than OPIM-C on several datasets and shows strong generalization ability. Finally, we conduct a large number of experiments on synthetic and realistic datasets and experimental results prove the effectiveness and superiority of our model.

Social networks allow rapid spread of ideas and innovations while negative information can also propagate widely. When a user receives two opposing opinions, they tend to believe the one arrives first. Therefore, once misinformation or rumor is detected, one containment method is to introduce a positive cascade competing against the rumor. Given a budget $k$, the rumor blocking problem asks for $k$ seed users to trigger the spread of a positive cascade such that the number of the users who are not influenced by rumor can be maximized. The prior works have shown that the rumor blocking problem can be approximated within a factor of $(1 - 1/e)$ by a classic greedy algorithm combined with Monte Carlo simulation. Unfortunately, the Monte Carlo simulation based methods are time consuming and the existing algorithms either trade performance guarantees for practical efficiency or vice versa. In this paper, we present a randomized approximation algorithm which is provably superior to the state-of-the art methods with respect to running time. The superiority of the proposed algorithm is demonstrated by experiments done on both the real-world and synthetic social networks.

Blockchain can provide a dependable environment for the Internet of Things (IoT), while the high computing power and energy required by blockchain hinder its applications in IoT. Offloading the computation at the resource-limited IoT devices to a cloud/edge computing service provider (CESP) is a feasible solution to the execution of computation-intensive blockchain tasks. The CESP provides computing resources to IoT users with a cloud and multiple edge servers that work collaboratively such that the users are able to perform mobile blockchain services. Resource allocation and pricing of computing resources at the cloud/edges have a significant impact on the revenues of CESP and users. Most of the existing works on the cooperative edge-cloud for computation offloading assumes that a user is mapped to a prespecified edge server or the cloud. However, the CESP may choose a server from either the edge servers or the cloud to run the offloaded tasks by jointly considering the cost and income of the service provisioning. In this article, we formulate a Stackelberg game with CESP as the leader and users as the followers for cloud/edge computing resource management. We prove the existence of Stackelberg equilibrium and analyze the equilibrium. We then model the resource allocation and pricing at the CESP as a mixed-integer programming problem (MIP) with the objective to optimize the CESP's revenue and propose an efficient iterative greedy-and-search-based resource allocation and pricing algorithm (IGS). The algorithm solves two subproblems comprising the CESP's revenue optimization problem: resource allocation under a given resource price and resource pricing based on a specified resource allocation scheme. The first subproblem evaluates where to execute the computing tasks via a greedy-and-search-based approach, whereas the second subproblem estimates the resource price through golden section search. We conduct experiments through simulations. Simulation results show that the proposed algorithm can effectively improve the revenue of both the CESP and the IoT terminals.

Online social networks such as Facebook, Twitter and Wechat have become major social tools. The users can not only keep in touch with family and friends, but also send and share the instant information. However, in some practical scenarios, we need to take effective measures to control the negative information spreading, e.g, rumors spread over the networks. In this paper, we first propose the Minimizing Influence of Rumors (MIR) problem, i.e., selecting a blocker set $\mathcal{B}$ with $k$ nodes such that the users' total activation probability by rumor source set $s$ is minimized. Then we employ the classical Independent Cascade (IC) model as information diffusion model. Based on the IC model, we prove the objective function is monotone decreasing and non-submodular. To address the MIR problem effectively, we propose a two-stages method enerating Candidate Set $\&$ Selecting Blockers (GCSSB) for the general networks. Furthermore, we also study the MIR problem on the tree network and propose a dynamic programming guaranteeing the optimal solution. Finally, we evaluate proposed algorithms by simulations on synthetic and real-life social networks, respectively. Experimental results show our algorithms are superior to the comparative heuristic approaches such as ut-Degree (OD), Betweenness Centrality (BC) and PageRank (PR).