Nonsubmodular Constrained Profit Maximization in Attribute Networks

The number of social individuals who interact with their friends through social networks is increasing, leading to an undeniable fact that word-of-mouth marketing has become one of the useful ways to promote sale of products. The Constrained Profit Maximization in Attribute network (CPMA) problem, as an extension of the classical influence maximization problem, is the main focus of this paper. We propose the profit maximization in attribute network problem under a cardinality constraint which is closer to the actual situation. The profit spread metric of CPMA calculates the total benefit and cost generated by all the active nodes. Different from the classical Influence Maximization problem, the influence strength should be recalculated according to the emotional tendency and classification label of nodes in attribute networks. The profit spread metric is no longer monotone and submodular in general. Given that the profit spread metric can be expressed as the difference between two submodular functions and admits a DS decomposition, a three-phase algorithm named as Marginal increment and Community-based Prune and Search(MCPS) Algorithm frame is proposed which is based on Louvain algorithm and logistic function. Due to the method of marginal increment, MPCS algorithm can compute profit spread more directly and accurately. Experiments demonstrate the effectiveness of MCPS algorithm.

Efficient Targeted Influence Maximization Based on Multidimensional Selection in Social Networks

The influence maximization problem over social networks has become a popular research problem, since it has many important practical applications such as online advertising, virtual market, and so on. General influence maximization problem is defined over the whole network, whose intuitive aim is to find a seed node set with size at most k in order to affect as many as nodes in the network. However, in real applications, it is commonly required that only special nodes (target) in the network are expected to be influenced, which can use the same cost of placing seed nodes but influence more targeted nodes really needed. Some research efforts have provided solutions for the corresponding targeted influence maximization problem (TIM for short). However, there are two main drawbacks of previous works focusing on the TIM problem. First, some works focusing on the case the targets are given arbitrarily make it hard to achieve efficient performance guarantee required by real applications. Second, some previous works studying the TIM problems by specifying the target set in a probabilistic way is not proper for the case that only exact target set is required. In this paper, we study the Multidimensional Selection based Targeted Influence Maximization problem, MSTIM for short. First, the formal definition of the problem is given based on a brief and expressive fragment of general multi-dimensional queries. Then, a formal theoretical analysis about the computational hardness of the MSTIM problem shows that even for a very simple case that the target set specified is 1 larger than the seed node set, the MSTIM problem is still NP-hard. Then, the basic framework of RIS (short for Reverse Influence Sampling) is extended and shown to have a 1 − 1/e − ϵ approximation ratio when a sampling size is satisfied. To satisfy the efficiency requirements, an index-based method for the MSTIM problem is proposed, which utilizes the ideas of reusing previous results, exploits the covering relationship between queries and achieves an efficient solution for MSTIM. Finally, the experimental results on real datasets show that the proposed method is indeed rather efficient.

Community-based framework for influence maximization problem in social networks

<p>Given a social graph, the influence maximization problem (IMP) is the act of selecting a group of nodes that cause maximum influence if they are considered as seed nodes of a diffusion process. IMP is an active research area in social network analysis due to its practical need in applications like viral marketing, target advertisement, and recommendation system. In this work, we propose an efficient solution for IMP based on the social network structure. The community structure is a property of real-world graphs. In fact, communities are often overlapping because of the involvement of users in many groups (family, workplace, and friends). These users are represented by overlapped nodes in the social graphs and they play a special role in the information diffusion process. This fact prompts us to propose a solution framework consisting of three phases: firstly, the community structure is discovered, secondly, the candidate seeds are generated, then lastly the set of final seed nodes are selected. The aim is to maximize the influence with the community diversity of influenced users. The study was validated using synthetic as well as real social network datasets. The experimental results show improvement over baseline methods and some important conclusions were reported.</p>

Link-based influence maximization in networks of health promotion professionals

The influence maximization problem (IMP) as classically formulated is based on the strong assumption that “chosen” nodes always adopt the new product. In this paper we propose a new influence maximization problem, referred to as the “Link-based Influence Maximization Problem” (LIM), which differs from IMP in that the decision variable of the spreader has changed from choosing an optimal seed to selecting an optimal node to influence in order to maximize the spread. Based on our proof that LIM is NP-hard with a monotonic increasing and submodular target function, we propose a greedy algorithm, GLIM, for optimizing LIM and use numerical simulation to explore the performance in terms of spread and computation time in different network types. The results indicate that the performance of LIM varies across network types. We illustrate LIM by applying it in the context of a Dutch national health promotion program for prevention of youth obesity within a network of Dutch schools. GLIM is seen to outperform the other methods in all network types at the cost of a higher computation time. These results suggests that GLIM may be utilized to increase the effectiveness of health promotion programs.

Adaptive Influence Maximization

Influence maximization problem attempts to find a small subset of nodes that makes the expected influence spread maximized, which has been researched intensively before. They all assumed that each user in the seed set we select is activated successfully and then spread the influence. However, in the real scenario, not all users in the seed set are willing to be an influencer. Based on that, we consider each user associated with a probability with which we can activate her as a seed, and we can attempt to activate her many times. In this article, we study the adaptive influence maximization with multiple activations (Adaptive-IMMA) problem, where we select a node in each iteration, observe whether she accepts to be a seed, if yes, wait to observe the influence diffusion process; if no, we can attempt to activate her again with a higher cost or select another node as a seed. We model the multiple activations mathematically and define it on the domain of integer lattice. We propose a new concept, adaptive dr-submodularity, and show our Adaptive-IMMA is the problem that maximizing an adaptive monotone and dr-submodular function under the expected knapsack constraint. Adaptive dr-submodular maximization problem is never covered by any existing studies. Thus, we summarize its properties and study its approximability comprehensively, which is a non-trivial generalization of existing analysis about adaptive submodularity. Besides, to overcome the difficulty to estimate the expected influence spread, we combine our adaptive greedy policy with sampling techniques without losing the approximation ratio but reducing the time complexity. Finally, we conduct experiments on several real datasets to evaluate the effectiveness and efficiency of our proposed policies.