Given a social network with nonuniform selection cost of the users, the problem of \textit{Budgeted Influence Maximization} (BIM in short) asks for selecting a subset of the nodes within an allocated budget for initial activation, such that due to the cascading effect, influence in the network is maximized. In this paper, we study this problem with a variation, where a set of nodes are designated as target nodes, each of them is assigned with a benefit value, that can be earned by influencing them, and our goal is to maximize the earned benefit by initially activating a set of nodes within the budget. We call this problem as the \textsc{Earned Benefit Maximization Problem}. First, we show that this problem is NP\mbox{-}Hard and the benefit function is \textit{monotone}, \textit{sub\mbox{-}modular} under the \textit{Independent Cascade Model} of diffusion. We propose an incremental greedy strategy for this problem and show, with minor modification it gives $(1-\frac{1}{\sqrt{e}})$\mbox{-}factor approximation guarantee on the earned benefit. Next, by exploiting the sub\mbox{-}modularity property of the benefit function, we improve the efficiency of the proposed greedy algorithm. Then, we propose a hop\mbox{-}based heuristic method, which works based on the computation of the `expected earned benefit' of the effective neighbors corresponding to the target nodes. Finally, we perform a series of extensive experiments with four real\mbox{-}life, publicly available social network datasets. From the experiments, we observe that the seed sets selected by the proposed algorithms can achieve more benefit compared to many existing methods. Particularly, the hop\mbox{-}based approach is found to be more efficient than the other ones for solving this problem.
In this paper, we study the Budgeted Influence Maximization with Delay Problem, for which the number of literature are limited. We propose an approximate marginal spread computation\mbox{-}based approach for solving this problem. The proposed methodology has been implemented with three benchmark social network datasets and the obtained results are compared with the existing methods from the literature. Experimental results show that the proposed approach is able to select seed nodes which leads to more number of influential nodes with reasonable computational time.
In a social network, influence maximization is the problem of identifying a set of users that own the maximum {\it influence ability} across the network. In this paper, a novel credit distribution (CD) based model, termed as the multi-action CD (mCD) model, is introduced to quantify the influence ability of each user, which works with practical datasets where one type of action could be recorded for multiple times. Based on this model, influence maximization is formulated as a submodular maximization problem under a general knapsack constraint, which is NP-hard. An efficient streaming algorith…
Given a budget and arbitrary cost for selecting each node, the budgeted influence maximization (BIM) problem concerns selecting a set of seed nodes to disseminate some information that maximizes the total number of nodes influenced (termed as influence spread) in social networks at a total cost no more than the budget. Our proposed seed selection algorithm for the BIM problem guarantees an approximation ratio of (1 - 1/sqrt(e)). The seed selection algorithm needs to calculate the influence spread of candidate seed sets, which is known to be #P-complex. Identifying the linkage between the compu…
Due to much closer to real application scenarios,the budgeted influence maximization (BIM) problem has attracted great attention among researchers. As a variant of the influence maximization (IM) problem, the BIM problem aims at mining several nodes with different costs as seeds with limited budget to maximize the influence as possible. By first activating these seed nodes and spreading influence under the given propagation model, the maximized spread of influence can be reached in the network. Several approaches have been proposed for BIM. Most of them are modified versions of the greedy algo…
Today, many companies take advantage of viral marketing to promote their new products, and since there are several competing companies in many markets, Competitive Influence Maximization has attracted much attention. Two categories of studies exist in the literature. First, studies that focus on which nodes from the network to select considering the existence of the opponents. Second, studies that focus on the problem of budget allocation. In this work, we integrate these two lines of research and propose a new scenario where competition happens in two phases. First, parties identify the most …
In this paper, we study influence maximization in the voter model in the presence of biased voters (or zealots) on complex networks. Under what conditions should an external controller with finite budget who aims at maximizing its influence over the system target zealots? Our analysis, based on both analytical and numerical results, shows a rich diagram of preferences and degree-dependencies of allocations to zealots and normal agents varying with the budget. We find that when we have a large budget or for low levels of zealotry, optimal strategies should give larger allocations to zealots and…
Continuous influence maximization (CIM) generalizes the original influence maximization by incorporating general marketing strategies: a marketing strategy mix is a vector $\boldsymbol x = (x_1,\dots,x_d)$ such that for each node $v$ in a social network, $v$ could be activated as a seed of diffusion with probability $h_v(\boldsymbol x)$, where $h_v$ is a strategy activation function satisfying DR-submodularity. CIM is the task of selecting a strategy mix $\boldsymbol x$ with constraint $\sum_i x_i \le k$ where $k$ is a budget constraint, such that the total number of activated nodes after the …
The typical algorithmic problem in viral marketing aims to identify a set of influential users in a social network, who, when convinced to adopt a product, shall influence other users in the network and trigger a large cascade of adoptions. However, the host (the owner of an online social platform) often faces more constraints than a single product, endless user attentions, unlimited budget and unbounded time; in reality, multiple products need to be advertised, each user can tolerate only a small number of recommendations, influencing user has a cost and advertisers have only limited budgets,…
Given a social network of users with selection cost, the \textsc{Budgeted Influence Maximization Problem} (\emph{BIM Problem} in short) asks for selecting a subset of the nodes (known as \emph{seed nodes}) within an allocated budget for initial activation to maximize the influence in the network. In this paper, we study this problem under the \emph{co\mbox{-}operative game theoretic} framework. We model this problem as a co\mbox{-}operative game where the users of the network are the players and for a group of users, the expected influence by them under the \emph{Maximum Influence Arborences} …
Delhi Technological University（德里理工大学）；University of Technology Sydney（悉尼科技大学）
In recent years, social networking platforms have gained significant popularity among the masses like connecting with people and propagating ones thoughts and opinions. This has opened the door to user-specific advertisements and recommendations on these platforms, bringing along a significant focus on Influence Maximisation (IM) on social networks due to its wide applicability in target advertising, viral marketing, and personalized recommendations. The aim of IM is to identify certain nodes in the network which can help maximize the spread of certain information through a diffusion cascade. …
A popular model to measure the stability of a network is k-core - the maximal induced subgraph in which every vertex has at least k neighbors. Many studies maximize the number of vertices in k-core to improve the stability of a network. In this paper, we study the edge k-core problem: Given a graph G, an integer k and a budget b, add b edges to non-adjacent vertex pairs in G such that the k-core is maximized. We prove the problem is NP-hard and APX-hard. A heuristic algorithm is proposed on general graphs with effective optimization techniques. Comprehensive experiments on 9 real-life datasets…
Influence maximization is the task of finding k seed nodes in a social network such that the expected number of activated nodes in the network (under certain influence propagation model), referred to as the influence spread, is maximized. Lattice influence maximization (LIM) generalizes influence maximization such that, instead of selecting k seed nodes, one selects a vector x = (x_1, ..., x_d) from a discrete space X called a lattice, where x_j corresponds to the j-th marketing strategy and x represents a marketing strategy mix. Each strategy mix x has probability h_u(x) to activate a node u …
In the problem of influence maximization in information networks, the objective is to choose a set of initially active nodes subject to some budget constraints such that the expected number of active nodes over time is maximized. The linear threshold model has been introduced to study the opinion cascading behavior, for instance, the spread of products and innovations. In this paper, we we extends the classic linear threshold model [18] to capture the non-progressive be- havior. The information maximization problem under our model is proved to be NP-Hard, even for the case when the underlying …
Revenue maximization (RM) is one of the most important problems on online social networks (OSNs), which attempts to find a small subset of users in OSNs that makes the expected revenue maximized. It has been researched intensively before. However, most of exsiting literatures were based on non-adaptive seeding strategy and on simple information diffusion model, such as IC/LT-model. It considered the single influenced user as a measurement unit to quantify the revenue. Until Collaborate Game model appeared, it considered activity as a basic object to compute the revenue. An activity initiated b…
The research of influence propagation in social networks via word-of-mouth processes has been given considerable attention in recent years. Arguably, the most fundamental problem in this domain is influence maximization, where the goal is to identify a seed set of individuals that can trigger a large cascade of influence in the network. While there has been significant progress regarding this problem and its variants, one basic shortcoming of the models is that they lack the flexibility in the way the budget is allocated to individuals. Indeed, budget allocation is a critical issue in advertis…
Google Research（谷歌研究院）；Princeton University（普林斯顿大学）；Carnegie Mellon University（卡内基梅隆大学）；MPI for Software Systems（马克斯·普朗克软件系统研究所）；Georgia Institute of Technology（佐治亚理工学院）
A typical viral marketing model identifies influential users in a social network to maximize a single product adoption assuming unlimited user attention, campaign budgets, and time. In reality, multiple products need campaigns, users have limited attention, convincing users incurs costs, and advertisers have limited budgets and expect the adoptions to be maximized soon. Facing these user, monetary, and timing constraints, we formulate the problem as a submodular maximization task in a continuous-time diffusion model under the intersection of a matroid and multiple knapsack constraints. We prop…
Social advertising (or social promotion) is an effective approach that produces a significant cascade of adoption through influence in the online social networks. The goal of this work is to optimize the ad allocation from the platform's perspective. On the one hand, the platform would like to maximize revenue earned from each advertiser by exposing their ads to as many people as possible, one the other hand, the platform wants to reduce free-riding to ensure the truthfulness of the advertiser. To access this tradeoff, we adopt the concept of \emph{regret} \citep{viral2015social} to measure th…
Incentivized social advertising, an emerging marketing model, provides monetization opportunities not only to the owners of the social networking platforms but also to their influential users by offering a "cut" on the advertising revenue. We consider a social network (the host) that sells ad-engagements to advertisers by inserting their ads, in the form of promoted posts, into the feeds of carefully selected "initial endorsers" or seed users: these users receive monetary incentives in exchange for their endorsements. The endorsements help propagate the ads to the feeds of their followers. In …
The link recommendation problem consists in suggesting a set of links to the users of a social network in order to increase their social circles and the connectivity of the network. Link recommendation is extensively studied in the context of social networks and of general complex networks due to its wide range of applications. Most of the existing link recommendation methods estimate the likelihood that a link is adopted by users and recommend links that are likely to be established. However, most of such methods overlook the impact that the suggested links have on the capability of the netwo…
The optimal allocation of resources for maximizing influence, spread of information or coverage, has gained attention in the past years, in particular in machine learning and data mining. But in applications, the parameters of the problem are rarely known exactly, and using wrong parameters can lead to undesirable outcomes. We hence revisit a continuous version of the Budget Allocation or Bipartite Influence Maximization problem introduced by Alon et al. (2012) from a robust optimization perspective, where an adversary may choose the least favorable parameters within a confidence set. The resu…
Purdue University（普渡大学）；University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）；Iowa State University（爱荷华州立大学）；KAUST（阿卜杜拉国王科技大学）
We consider the problem of Influence Maximization (IM), the task of selecting $k$ seed nodes in a social network such that the expected number of nodes influenced is maximized. We propose a community-aware divide-and-conquer framework that involves (i) learning the inherent community structure of the social network, (ii) generating candidate solutions by solving the influence maximization problem for each community, and (iii) selecting the final set of seed nodes using a novel progressive budgeting scheme. Our experiments on real-world social networks show that the proposed framework outperfor…
Reliable propagation of information through large networks, e.g., communication networks, social networks or sensor networks is very important in many applications concerning marketing, social networks, and wireless sensor networks. However, social ties of friendship may be obsolete, and communication links may fail, inducing the notion of uncertainty in such networks. In this paper, we address the problem of optimizing information propagation in uncertain networks given a constrained budget of edges. We show that this problem requires to solve two NP-hard subproblems: the computation of expec…
For maximizing influence spread in a social network, given a certain budget on the number of seed nodes, we investigate the effects of selecting and activating the seed nodes in multiple phases. In particular, we formulate an appropriate objective function for two-phase influence maximization under the independent cascade model, investigate its properties, and propose algorithms for determining the seed nodes in the two phases. We also study the problem of determining an optimal budget-split and delay between the two phases.
In the adaptive influence maximization problem, we are given a social network and a budget $k$, and we iteratively select $k$ nodes, called seeds, in order to maximize the expected number of nodes that are reached by an influence cascade that they generate according to a stochastic model for influence diffusion. Differently from the non-adaptive influence maximization problem, where all the seeds must be selected beforehand, here nodes are selected sequentially one by one, and the decision on the $i$th seed is based on the observed cascade produced by the first $i-1$ seeds. We focus on the myo…
Social media sites are now becoming very important platforms for product promotion or marketing campaigns. Therefore, there is broad interest in determining ways to guide a site to react more positively to a product with a limited budget. However, the practical significance of the existing studies on this subject is limited for two reasons. First, most studies have investigated the issue in oversimplified networks in which several important network characteristics are ignored. Second, the opinions of individuals are modeled as bipartite states(e.g., support or not) in numerous studies, however…
Influence maximization serves as the main goal of a variety of social network activities such as viral marketing and campaign advertising. The independent cascade model for the influence spread assumes a one-time chance for each activated node to influence its neighbors. This reasonable assumption cannot be bypassed, since otherwise the influence probabilities of the nodes, modeled by the edge weights, would be altered. On the other hand, the manually activated seed set nodes can be reselected without violating the model parameters or assumptions. The reselection of a seed set node, simply mea…
The University of Hong Kong（香港大学）；Tsinghua University（清华大学）
Social networks have been popular platforms for information propagation. An important use case is viral marketing: given a promotion budget, an advertiser can choose some influential users as the seed set and provide them free or discounted sample products; in this way, the advertiser hopes to increase the popularity of the product in the users' friend circles by the world-of-mouth effect, and thus maximizes the number of users that information of the production can reach. There has been a body of literature studying the influence maximization problem. Nevertheless, the existing studies mostly…
Most previous work on influence maximization in social networks is limited to the non-adaptive setting in which the marketer is supposed to select all of the seed users, to give free samples or discounts to, up front. A disadvantage of this setting is that the marketer is forced to select all the seeds based solely on a diffusion model. If some of the selected seeds do not perform well, there is no opportunity to course-correct. A more practical setting is the adaptive setting in which the marketer initially selects a batch of users and observes how well seeding those users leads to a diffusio…
SP-GCRL: Influence Maximization on Incomplete Social Graphs
School of Systems Science and Engineering（系统科学与工程学院）；Sun Yat-sen University（中山大学）；Jiangxi University of Finance and Economics（江西财经大学）；The Hong Kong Polytechnic University（香港理工大学）；Anhui University of Science and Technology（安徽理工大学）
In signed networks, each edge is labeled as either positive or negative. The edge sign captures the polarity of a relationship. Balance of signed networks is a well-studied property in graph theory. In a balanced (sub)graph, the vertices can be partitioned into two subsets with negative edges present only across the partitions. Balanced portions of a graph have been shown to increase coherence among its members and lead to better performance. While existing works have focused primarily on finding the largest balanced subgraph inside a graph, we study the network design problem of maximizing ba…
Finding influential users in social networks is a fundamental problem with many possible useful applications. Viewing the social network as a graph, the influence of a set of users can be measured by the number of neighbors located within a given number of hops in the network, where each hop marks a step of influence diffusion. In this paper, we reduce the problem of IM to a budget-constrained d-hop dominating set problem (kdDSP). We propose a unified machine learning (ML) framework, FastCover, to solve kdDSP by learning an efficient greedy strategy in an unsupervised way. As one critical comp…
Influence maximization (IM) is a combinatorial problem of identifying a subset of nodes called the seed nodes in a network (graph), which when activated, provide a maximal spread of influence in the network for a given diffusion model and a budget for seed set size. IM has numerous applications such as viral marketing, epidemic control, sensor placement and other network-related tasks. However, the uses are limited due to the computational complexity of current algorithms. Recently, learning heuristics for IM have been explored to ease the computational burden. However, there are serious limit…
Social networks are commonly used for marketing purposes. For example, free samples of a product can be given to a few influential social network users (or "seed nodes"), with the hope that they will convince their friends to buy it. One way to formalize marketers' objective is through influence maximization (or IM), whose goal is to find the best seed nodes to activate under a fixed budget, so that the number of people who get influenced in the end is maximized. Recent solutions to IM rely on the influence probability that a user influences another one. However, this probability information m…
In this paper, we investigate the discount allocation problem in social networks. It has been reported that 40\% of consumers will share an email offer with their friend and 28\% of consumers will share deals via social media platforms. What does this mean for a business? Essentially discounts should not just be treated as short term solutions to attract individual customer, instead, allocating discounts to a small fraction of users (called seed users) may trigger a large cascade in a social network. This motivates us to study the influence maximization discount allocation problem: given a soc…
IM-META: Influence Maximization Using Node Metadata in Networks With Unknown Topology
Dankook University（檀国大学）；Yonsei University（延世大学）；Posts and Telecommunications Institute of Technology（邮电技术学院）；Pohang University of Science and Technology (POSTECH)（浦项科技大学）；University of Konstanz（康斯坦茨大学）
