Locally adaptive optimization: adaptive seeding for monotone submodular functions

The Adaptive Seeding problem is an algorithmic challenge motivated by influence maximization in social networks: One seeks to select among certain accessible nodes in a network, and then select, adaptively, among neighbors of those nodes as they become accessible in order to maximize a global objective function. More generally, adaptive seeding is a stochastic optimization framework where the choices in the first stage affect the realizations in the second stage, over which we aim to optimize. Our main result is a $(1-1/e)^2$-approximation for the adaptive seeding problem for any monotone submodular function. While adaptive policies are often approximated via non-adaptive policies, our algorithm is based on a novel method we call \emph{locally-adaptive} policies. These policies combine a non-adaptive global structure, with local adaptive optimizations. This method enables the $(1-1/e)^2$-approximation for general monotone submodular functions and circumvents some of the impossibilities associated with non-adaptive policies. We also introduce a fundamental problem in submodular optimization that may be of independent interest: given a ground set of elements where every element appears with some small probability, find a set of expected size at most $k$ that has the highest expected value over the realization of the elements. We show a surprising result: there are classes of monotone submodular functions (including coverage) that can be approximated almost optimally as the probability vanishes. For general monotone submodular functions we show via a reduction from \textsc{Planted-Clique} that approximations for this problem are not likely to be obtainable. This optimization problem is an important tool for adaptive seeding via non-adaptive policies, and its hardness motivates the introduction of \emph{locally-adaptive} policies we use in the main result.

In recent years, due to the surge in popularity of social-networking web sites, considerable interest has arisen regarding influence maximization in social networks. Given a social network structure, the problem of influence maximization is to determine a minimum set of nodes that could maximize the spread of influences. With a large-scale social network, the efficiency and practicability of such algorithms are critical. Although many recent studies have focused on the problem of influence maximization, these works in general are time-consuming when a social network is large-scale. In this paper, we propose two novel algorithms, CDH-Kcut and Community and Degree Heuristic on Kcut/SHRINK, to solve the influence maximization problem based on a realistic model. The algorithms utilize the community structure, which significantly decreases the number of candidates of influential nodes, to avoid information overlap. The experimental results on both synthetic and real datasets indicate that our algorithms not only significantly outperform the state-of-the-art algorithms in efficiency but also possess graceful scalability.

Most of the recent online social media collects a huge volume of data not just about who is linked with whom (aka link data) but also, about who is interacting with whom (aka interaction data). The presence of both variety and volume in these datasets pose new challenges while conducting social network analysis. In particular, we present a general framework to deal with both variety and volume in the data for a key social network analysis task - Influence Maximization. The well known influence maximization problem [15] (or viral marketing through social networks) deals with selecting a few influential initial seeds to maximize the awareness of product(s) over the social network. As it is computationally hard [15], a greedy approximation algorithm is designed to address the influence maximization problem. However, the major drawback of this greedy algorithm is that it runs extremely slow even on network datasets consisting of a few thousand nodes and edges [20,6]. Several efficient heuristics have been proposed in the literature [6] to alleviate this computational difficulty; however these heuristics are designed for specific influence propagation models such as linear threshold model and independent cascade model. This motivates the strong need to design an approach that not only works with any influence propagation model, but also efficiently solves the influence maximization problem. In this paper, we precisely address this problem by proposing a new framework which fuses both link and interaction data to come up with a backbone for a given social network, which can further be used for efficient influence maximization. We then conduct thorough experimentation with several real life social network datasets such as DBLP, Epinions, Digg, and Slashdot and show that the proposed approach is efficient as well as scalable.KeywordsSocial networksinfluence maximizationviral marketingsparsification

Influence maximization is an optimization problem that aims at finding a small set of nodes as seed nodes to maximize the spread of influence in a social network. In this paper, we introduce a new technique called Non-backtracking Random Walk into the influence maximization problem. An optimized algorithm, called NBRW, is devised through sampling nodes when applying restricted non-backtracking walk in network communities. Node's traversing number gives a good estimate of its influence. Our algorithm can be executed in linear time, which beats other influence maximization algorithms. We give extensive experiments under various diffusion models against other state-of-the-art node-selection algorithms. It demonstrates that in terms of influence range and convergent speed our algorithm gives a superior performance under most diffusion models, especially for linear threshold model.

Using swarm intelligence algorithms to detect influential individuals for influence maximization in social networks

The popularity of social networks has grown manifolds in recent years because of various activities like fast propagation of ideas, publicity, and news. Influence maximization (IM) is one of the most highly studied problems in the field of social network analysis due to its business values. Influence maximization aims to identify influential nodes that can spread the information to the maximum number of nodes in the network through diffusion cascade. Traditional methods for IM include centrality based and greedy based measures. However, each method has some limitations. Recently, some methods of IM are introduced, which consider the presence of community structure in networks. Community structure has a significant impact on information diffusion, because of dense connections between the nodes in the community. In this paper, we propose a novel influence maximization algorithm using node seeding, label propagation, and community detection. We first use extended h-index centrality to detect the seed nodes and then use the label propagation technique to detect communities. Further, we merge smaller and related communities to a larger community with the help of a relationship matrix. Finally, top-k influential nodes from these communities are identified. These ideas lead to our proposed algorithm: Influence Maximization using Extended h-index, and Label Propagation with Relationship matrix (IM-ELPR). We adopt Independent Cascade (IC) information diffusion model to spread the information originating from chosen influential nodes. The proposed algorithm intends to identify influential nodes from different communities globally and does not depend on the specific community’s antecedent structural information. Experimental results performed on several real-life data sets reveal that the proposed algorithm performs better than many other existing popular algorithms.

In recent years, Influence Maximization (IM) has gained great research interest in the field of social network research. The IM is a viral marketing based approach to find the influential users on the social networks. It determines a small seed set that can activate a maximum number of nodes in the network under some diffusion models such as Linear Threshold model or Independent Cascade model. However, previous works have not focused on the opportunity cost defined by the minimum number of nodes that must be motivated in order to activate the initial seed nodes. In this work, we have introduced a Reverse Influence Maximization (RIM) problem to estimate the opportunity cost. The RIM, working in opposite manner to IM, calculates the opportunity cost for viral marketing in the social networks. We have proposed the Extended Randomized Linear Threshold RIM (ERLT-RIM) model to solve the RIM problem. The ERLT-RIM is a Linear Threshold (LT)-based model which is an extension to the existing RLT-RIM model. We also have evaluated the performance of the algorithm using three real-world datasets. The result shows that the proposed model determines the optimal opportunity cost with time efficiency as compared to existing models.

Information diffusion has been a crucial issue in social network research. The influence maximization problem asks for ways to identify nodes that are able to maximally diffuse information through a network. Recently, game-theoretical methods emerged that partitions a network into coalitions, and facilitate influence maximization. A notable example is a method based on Shapley value [13]. A major disadvantage with this approach is the lack of consideration of externality on coalition formation. In this paper, we propose consensus value for influence maximization (CVIM) to overcome this limitation. After forming coalitions using consensus value, the method selects initial coalitions based on the gain of each coalition, and finally chooses seed nodes in the selected coalitions. Empirical evidence over several real-world networks demonstrates that CVIM produces better results of influence maximization while significantly reducing the running time as compared to existing approaches.

The evolution and spread of social networks have attracted the interest of the scientific community in the last few years. Specifically, several new interesting problems, which are hard to solve, have arisen in the context of viral marketing, disease analysis, and influence analysis, among others. Companies and researchers try to find the elements that maximize profit, stop pandemics, etc. This family of problems is collected under the term Social Network Influence Maximization problem (SNIMP), whose goal is to find the most influential users (commonly known as seeds) in a social network, simulating an influence diffusion model. SNIMP is known to be an mathcal {NP}-hard problem and, therefore, an exact algorithm is not suitable for solving it optimally in reasonable computing time. The main drawback of this optimization problem lies on the computational effort required to evaluate a solution. Since each node is infected with a certain probability, the objective function value must be calculated through a Monte Carlo simulation, resulting in a computationally complex process. The current proposal tries to overcome this limitation by considering a metaheuristic algorithm based on the Greedy Randomized Adaptive Search Procedure (GRASP) framework to design a quick solution procedure for the SNIMP. Our method consists of two distinct stages: construction and local search. The former is based on static features of the network, which notably increases its efficiency since it does not require to perform any simulation during construction. The latter involves a local search based on an intelligent neighborhood exploration strategy to find the most influential users based on swap moves, also aiming for an efficient processing. Experiments performed on 7 well-known social network datasets with 5 different seed set sizes confirm that the proposed algorithm is able to provide competitive results in terms of quality and computing time when comparing it with the best algorithms found in the state of the art.

Information diffusion and influence maximization are important and extensively studied problems in social networks. Various models and algorithms have been proposed in the literature in the context of the influence maximization problem. A crucial assumption in all these studies is that the influence probabilities are known to the social planner. This assumption is unrealistic since the influence probabilities are usually private information of the individual agents and strategic agents may not reveal them truthfully. Moreover, the influence probabilities could vary significantly with the type of the information flowing in the network and the time at which the information is propagating in the network. In this paper, we use a mechanism design approach to elicit influence probabilities truthfully from the agents. Our main contribution is to design a scoring rule based mechanism in the context of the influencer-influencee model. In particular, we show the incentive compatibility of the mechanisms and propose a reverse weighted scoring rule based mechanism as an appropriate mechanism to use.

Influence maximization deals with the problem of identifying k-size subset of nodes in a social network that can maximize the influence spread in the network. In this paper, the problem of influence maximization using two aspects, node connectivity and node activity level, has been studied. To measure node connectivity, the widely popular and intuitive measure of out-degree of node has been used, and for node activity, node’s past interactions have been taken into consideration. For studying influence spread, two activity-based diffusion models, namely Activity-based Independent Cascade model and Activity-based Linear Threshold model, have been proposed in which influence propagation is driven by a node’s activity that it has actually performed in the past. Activity-based models aim at studying influence spread by incorporating a more realistic aspect corresponding to user behavior. Motivated by the belief that activity is as important as connectivity, UAC-Rank algorithm for the identification of initial adopters has been proposed.

Social network analysis attracted interests from both the research and business communities for a strong potential and variety of applications. In addition, this interest has been fuelled by the large success of online social networking sites and the subsequent abundance of social network data produced. A key aspect in this research field is the influence maximization in social networks. In this paper we discuss an overview about the models and the approaches widely used to analyse social networks. In this context, we also discuss data preparation and privacy concerns also considering different kind of approaches based on centrality measures.

Efficient Influence Maximization in Social-Networks Under Independent Cascade Model

A discrete shuffled frog-leaping algorithm to identify influential nodes for influence maximization in social networks

Influence maximization problem is to find a small set of influential nodes in a social network, whose activation of information propagation can be maximized using one of the propagation models such as independent cascade model. This paper proposes a new method to solve this problem based on discretized linear automaton algorithm and simple greedy algorithm. Every allowable node in the social network is regarded as an action and the goal of the learning automaton is to select an optimal subset of actions. To speed up the convergence, firstly, the problem space is reduced by excluding the nodes lacking influence; then, the original learning process is divided into two parts: the sampling process and the learning process. Besides, a new scheme for determining the best parameters is presented, which is more applicable to practical problems. The obtained results show that the new proposed algorithm is efficient in real-life social networks. The results are close to the ones obtained by the greedy algorithm in terms of accuracy, and the new method greatly improves the speed of selecting the optimal subset.