Starting with the earliest studies showing that the spread of new trends, information, and innovations is closely related to the social influence exerted on people by their social networks, the research on social influence theory took off, providing remarkable evidence on social influence induced viral phenomena. Fueled by the extreme popularity of online social networks and social media, computational social influence has emerged as a subfield of data mining whose goal is to analyze and optimize social influence using computational frameworks such as algorithm design and theoretical modeling. One of the fundamental problems in this field is the problem of influence maximization, primarily motivated by the application of viral marketing. The objective is to identify a small set of users in a social network who, when convinced to adopt a product, shall influence others in the network in a manner that leads to a large number of adoptions.

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. Whenever any user engages with an ad, the host is paid some fixed amount by the advertiser, and the ad further propagates to the feed of her followers, potentially recursively. In this context, the problem for the host is is to allocate ads to influential users, taking into account the propensity of ads for viral propagation, and carefully apportioning the monetary budget of each of the advertisers between incentives to influential users and ad-engagement costs, with the rational goal of maximizing its own revenue. We show that, taking all important factors into account, the problem of revenue maximization in incentivized social advertising corresponds to the problem of monotone submodular function maximization, subject to a partition matroid constraint on the ads-to-seeds allocation, and submodular knapsack constraints on the advertisers' budgets. We show that this problem is NP-hard and devise two greedy algorithms with provable approximation guarantees, which differ in their sensitivity to seed user incentive costs. Our approximation algorithms require repeatedly estimating the expected marginal gain in revenue as well as in advertiser payment. By exploiting a connection to the recent advances made in scalable estimation of expected influence spread, we devise efficient and scalable versions of our two greedy algorithms. An extensive experimental assessment confirms the high quality of our proposal.

With the explosive growth of online social networks, it is now well understood that social information is highly helpful to recommender systems. Social recommendation methods are capable of battling the critical cold-start issue, and thus can greatly improve prediction accuracy. The main intuition is that through trust and influence, users are more likely to develop affinity toward items consumed by their social ties. Despite considerable work in social recommendation, little attention has been paid to the important distinctions between strong and weak ties, two well-documented notions in social sciences. In this work, we study the effects of distinguishing strong and weak ties in social recommendation. We use neighbourhood overlap to approximate tie strength and extend the popular Bayesian Personalized Ranking (BPR) model to incorporate the distinction of strong and weak ties. We present an EM-based algorithm that simultaneously classifies strong and weak ties in a social network w.r.t. optimal recommendation accuracy and learns latent feature vectors for all users and all items. We conduct extensive empirical evaluation on four real-world datasets and demonstrate that our proposed method significantly outperforms state-of-the-art pairwise ranking methods in a variety of accuracy metrics.

A key operation in network analysis is the discovery of cohesive subgraphs. The notion of $k$-truss has gained considerable popularity in this regard, based on its rich structure and efficient computability. However, many complex networks such as social, biological and communication networks feature uncertainty, best modeled using probabilities. Unfortunately the problem of discovering k-trusses in probabilistic graphs has received little attention to date. In this paper, given a probabilistic graph G, number k and parameter γ --(0,1], we define a (k,γ)-truss as a maximal connected subgraph H ⊆ G, in which for each edge, the probability that it is contained in at least (k-2) triangles is at least γ. We develop an efficient dynamic programming algorithm for decomposing a probabilistic graph into such maximal (k,γ)-trusses. The above definition of a (k,γ)-truss is local in that the "witness" graphs that has the (k-2) triangles containing an edge in H may be quite different for distinct edges. Hence, we also propose: a global (k,γ)-truss, which in addition to being a local (k,γ)-truss, has to satisfy the condition that the probability that H contains a k-truss is at least γ. We show that unlike local (k,γ)-trusses, the global (k,γ)-truss decomposition on a probabilistic graph is intractable. We propose a novel sampling technique which enables approximate discovery of global (k,γ)-trusses with high probability. Our extensive experiments on real datasets demonstrate the efficacy of our proposed approach and the usefulness of local and global (k,γ)-truss.

Social advertisement is one of the fastest growing sectors in the digital advertisement landscape: ads in the form of promoted posts are shown in the feed of users of a social networking platform, along with normal social posts; if a user clicks on a promoted post, the host (social network owner) is paid a fixed amount from the advertiser. In this context, allocating ads to users is typically performed by maximizing click-through-rate, i.e., the likelihood that the user will click on the ad. However, this simple strategy fails to leverage the fact the ads can propagate virally through the network, from endorsing users to their followers. In this paper, we study the problem of allocating ads to users through the viral-marketing lenses. We show that allocation that takes into account the propensity of ads for viral propagation can achieve significantly better performance. However, uncontrolled virality could be undesirable for the host as it creates room for exploitation by the advertisers: hoping to tap uncontrolled virality, an advertiser might declare a lower budget for its marketing campaign, aiming at the same large outcome with a smaller cost. This creates a challenging trade-off: on the one hand, the host aims at leveraging virality and the network effect to improve advertising efficacy, while on the other hand the host wants to avoid giving away free service due to uncontrolled virality. We formalize this as the problem of ad allocation with minimum regret, which we show is NP-hard and inapproximable w.r.t. any factor. However, we devise an algorithm that provides approximation guarantees w.r.t. the total budget of all advertisers. We develop a scalable version of our approximation algorithm, which we extensively test on four real-world data sets, confirming that our algorithm delivers high quality solutions, is scalable, and significantly outperforms several natural baselines.

Influence maximization is a well-studied problem that asks for a small set of influential users from a social network, such that by targeting them as early adopters, the expected total adoption through influence cascades over the network is maximized. However, almost all prior work focuses on cascades of a single propagating entity or purely-competitive entities. In this work, we propose the Comparative Independent Cascade (Com-IC) model that covers the full spectrum of entity interactions from competition to complementarity. In Com-IC, users' adoption decisions depend not only on edge-level information propagation, but also on a node-level automaton whose behavior is governed by a set of model parameters, enabling our model to capture not only competition, but also complementarity, to any possible degree. We study two natural optimization problems, Self Influence Maximization and Complementary Influence Maximization , in a novel setting with complementary entities. Both problems are NP-hard, and we devise efficient and effective approximation algorithms via non-trivial techniques based on reverse-reachable sets and a novel "sandwich approximation" strategy. The applicability of both techniques extends beyond our model and problems. Our experiments show that the proposed algorithms consistently outperform intuitive baselines on four real-world social networks, often by a significant margin. In addition, we learn model parameters from real user action logs.

Online platforms, such as Meetup and Plancast, have recently become popular for planning gatherings and event organization. However, there is a surprising lack of studies on how to effectively and efficiently organize social events for a large group of people through such platforms. In this paper, we study the key computational problem involved in organization of social events, to our best knowledge, for the first time.

People's interests are dynamically evolving, often affected by external factors such as trends promoted by the media or adopted by their friends. In this work, we model interest evolution through dynamic interest cascades: we consider a scenario where a user's interests may be affected by (a) the interests of other users in her social circle, as well as (b) suggestions she receives from a recommender system. In the latter case, we model user reactions through either attraction or aversion towards past suggestions. We study this interest evolution process, and the utility accrued by recommendations, as a function of the system's recommendation strategy. We show that, in steady state, the optimal strategy can be computed as the solution of a semi-definite program (SDP). Using datasets of user ratings, we provide evidence for the existence of aversion and attraction in real-life data, and show that our optimal strategy can lead to significantly improved recommendations over systems that ignore aversion and attraction.

Recommender Systems (RS) play a vital role in applications such as e-commerce and on-demand content streaming. Research on RS has mainly focused on the customer perspective , i.e., accurate prediction of user preferences and maximization of user utilities. As a result, most existing techniques are not explicitly built for revenue maximization , the primary business goal of enterprises. In this work, we explore and exploit a novel connection between RS and the profitability of a business. As recommendations can be seen as an information channel between a business and its customers, it is interesting and important to investigate how to make strategic dynamic recommendations leading to maximum possible revenue. To this end, we propose a novel revenue model that takes into account a variety of factors including prices, valuations, saturation effects, and competition amongst products. Under this model, we study the problem of finding revenue-maximizing recommendation strategies over a finite time horizon. We show that this problem is NP-hard, but approximation guarantees can be obtained for a slightly relaxed version, by establishing an elegant connection to matroid theory. Given the prohibitively high complexity of the approximation algorithm, we also design intelligent heuristics for the original problem. Finally, we conduct extensive experiments on two real and synthetic datasets and demonstrate the efficiency, scalability, and effectiveness our algorithms, and that they significantly outperform several intuitive baselines.

The key algorithmic problem in viral marketing is to identify a set of influential users (called seeds) in a social network, who, when convinced to adopt a product, shall influence other users in the network, leading to a large number of adoptions. When two or more players compete with similar products on the same network we talk about competitive viral marketing, which so far has been studied exclusively from the perspective of one of the competing players.

Influence maximization is a problem of finding a small set of highly influential users in a social network such that the spread of influence under certain propagation models is maximized. In this paper, we consider time-critical influence maximization, in which one wants to maximize influence spread within a given deadline. Since timing is considered in the optimization, we also extend the Independent Cascade (IC) model to incorporate the time delay aspect of influence diffusion in social networks. We show that time-critical influence maximization under the time-delayed IC model maintains desired properties such as submodularity, which allows a greedy algorithm to achieve an approximation ratio of 1-1/e, to circumvent the NP-hardness of the problem. To overcome the inefficiency of the approximation algorithm, we design two heuristic algorithms: the first one is based on a dynamic programming procedure that computes exact influence in tree structures, while the second one converts the problem to one in the original IC model and then applies existing fast heuristics to it. Our simulation results demonstrate that our heuristics achieve the same level of influence spread as the greedy algorithm while running a few orders of magnitude faster, and they also outperform existing algorithms that disregard the deadline constraint and delays in diffusion.

Influence maximization is the problem of finding a set of influential users in a social network such that the expected spread of influence under a certain propagation model is maximized. Much of the previous work has neglected the important distinction between social influence and actual product adoption. However, as recognized in the management science literature, an individual who gets influenced by social acquaintances may not necessarily adopt a product (or technology), due, e.g., to monetary concerns. In this work, we distinguish between influence and adoption by explicitly modeling the states of being influenced and of adopting a product. We extend the classical Linear Threshold (LT) model to incorporate prices and valuations, and factor them into users' decision-making process of adopting a product. We show that the expected profit function under our proposed model maintains submodularity under certain conditions, but no longer exhibits monotonicity, unlike the expected influence spread function. To maximize the expected profit under our extended LT model, we employ an unbudgeted greedy framework to propose three profit maximization algorithms. The results of our detailed experimental study on three real-world datasets demonstrate that of the three algorithms, PAGE, which assigns prices dynamically based on the profit potential of each candidate seed, has the best performance both in the expected profit achieved and in running time.

There is significant current interest in the problem of influence maximization: given a directed social network with influence weights on edges and a number k, find k seed nodes such that activating them leads to the maximum expected number of activated nodes, according to a propagation model. Kempe et al. showed, among other things, that under the Linear Threshold Model, the problem is NP-hard, and that a simple greedy algorithm guarantees the best possible approximation factor in PTIME. However, this algorithm suffers from various major performance drawbacks. In this paper, we propose SIMPATH, an efficient and effective algorithm for influence maximization under the linear threshold model that addresses these drawbacks by incorporating several clever optimizations. Through a comprehensive performance study on four real data sets, we show that SIMPATH consistently outperforms the state of the art w.r.t. running time, memory consumption and the quality of the seed set chosen, measured in terms of expected influence spread achieved.