Influence Maximization (IM), that seeks a small set of key users who spread the influence widely into the network, is a core problem in multiple domains. It finds applications in viral marketing, epidemic control, and assessing cascading failures within complex systems. Despite the huge amount of effort, IM in billion-scale networks such as Facebook, Twitter, and World Wide Web has not been satisfactorily solved. Even the state-of-the-art methods such as TIM+ and IMM may take days on those networks. In this paper, we propose SSA and D-SSA, two novel sampling frameworks for IM-based viral marketing problems. SSA and D-SSA are up to 1200 times faster than the SIGMOD'15 best method, IMM, while providing the same (1-1/e-ε) approximation guarantee. Underlying our frameworks is an innovative Stop-and-Stare strategy in which they stop at exponential check points to verify (stare) if there is adequate statistical evidence on the solution quality. Theoretically, we prove that SSA and D-SSA are the first approximation algorithms that use (asymptotically) minimum numbers of samples, meeting strict theoretical thresholds characterized for IM. The absolute superiority of SSA and D-SSA are confirmed through extensive experiments on real network data for IM and another topic-aware viral marketing problem, named TVM.

Social networks exhibit a very special property: community structure. Understanding the network community structure is of great advantages. It not only provides helpful information in developing more social-aware strategies for social network problems but also promises a wide range of applications enabled by mobile networking, such as routings in Mobile Ad Hoc Networks (MANETs) and worm containments in cellular networks. Unfortunately, understanding this structure is very challenging, especially in dynamic social networks where social activities and interactions are evolving rapidly. Can we quickly and efficiently identify the network community structure? Can we adaptively update the network structure based on previously known information instead of recomputing from scratch? In this paper, we present Quick Community Adaptation (QCA), an adaptive modularity-based method for identifying and tracing community structure of dynamic online social networks. Our approach has not only the power of quickly and efficiently updating network communities, through a series of changes, by only using the structures identified from previous network snapshots, but also the ability of tracing the evolution of community structure over time. To illustrate the effectiveness of our algorithm, we extensively test QCA on real-world dynamic social networks including ENRON email network, arXiv e-print citation network and Facebook network. Finally, we demonstrate the bright applicability of our algorithm via a realistic application on routing strategies in MANETs. The comparative results reveal that social-aware routing strategies employing QCA as a community detection core outperform current available methods.

Society relies heavily on its networked physical infrastructure and information systems. Accurately assessing the vulnerability of these systems against disruptive events is vital for planning and risk management. Existing approaches to vulnerability assessments of large-scale systems mainly focus on investigating inhomogeneous properties of the underlying graph elements. These measures and the associated heuristic solutions are limited in evaluating the vulnerability of large-scale network topologies. Furthermore, these approaches often fail to provide performance guarantees of the proposed solutions. In this paper, we propose a vulnerability measure, pairwise connectivity, and use it to formulate network vulnerability assessment as a graph-theoretical optimization problem, referred to as -disruptor. The objective is to identify the minimum set of critical network elements, namely nodes and edges, whose removal results in a specific degradation of the network global pairwise connectivity. We prove the NP-completeness and inapproximability of this problem and propose an pseudo-approximation algorithm to computing the set of critical nodes and an pseudo-approximation algorithm for computing the set of critical edges. The results of an extensive simulation-based experiment show the feasibility of our proposed vulnerability assessment framework and the efficiency of the proposed approximation algorithms in comparison to other approaches.

Online social networks have been one of the most effective platforms for marketing and advertising. Through the “world-of-mouth” exchanges, so-called viral marketing, the influence and product adoption can spread from few key influencers to billions of users in the network. To identify those key influencers, a great amount of work has been devoted for the Influence Maximization (IM) problem that seeks a set of k seed users that maximize the expected influence. Unfortunately, IM encloses two impractical assumptions: 1) any seed user can be acquired with the same cost and 2) all users are equally interested in the advertisement. In this paper, we propose a new problem, called Cost-aware Targeted Viral Marketing (CTVM), to find the most cost-effective seed users who can influence the most relevant users to the advertisement. Since CTVM is NP-hard, we design an efficient (1 - 1/√e-ϵ - e)-approximation algorithm, named BCT, to solve the problem in billion-scale networks. Comparing with IM algorithms, we show that BCT is both theoretically and experimentally faster than the state-of-the-arts while providing better solution quality. Moreover, we prove that under the Linear Threshold model, BCT is the first sub-linear time algorithm for CTVM (and IM) in dense networks. In our experiments with a Twitter dataset, containing 1.46 billions of social relations and 106 millions tweets, BCT can identify key influencers in each trending topic in only few minutes.

Online social networks (OSNs) provide a new platform for product promotion and advertisement. Influence maximization problem arisen in viral marketing has received a lot of attentions recently. Most of the existing diffusion models rely on one fundamental assumption that an influenced user necessarily adopts the product and encourages his/her friends to further adopt it. However, an influenced user may be just aware of the product. Due to personal preference, neutral or negative opinion can be generated so that product adoption is uncertain. Maximizing the total number of influenced users is not the uppermost concern, instead, letting more activated users hold positive opinions is of first importance. Motivated by above phenomenon, we proposed a model, called Opinion-based Cascading (OC) model. We formulate an opinion maximization problem on the new model to take individual opinion into consideration as well as capture the change of opinions at the same time. We show that under the OC model, opinion maximization is NP-hard and the objective function is no longer submodular. We further prove that there does not exist any approximation algorithm with finite ratio unless P=NP. We have designed an efficient algorithm to compute the total positive influence based on this new model. Comprehensive experiments on real social networks are conducted, and results show that previous methods overestimate the overall positive influence, while our model is able to distinguish between negative opinions and positive opinions, and estimate the overall influence more accurately.