Influence maximization has found applications in a wide range of real-world problems, for instance, viral marketing of products in an online social network, and information propagation of valuable information such as job vacancy advertisements and health-related information. While existing algorithmic techniques usually aim at maximizing the total number of people influenced, the population often comprises several socially salient groups, e.g., based on gender or race. As a result, these techniques could lead to disparity across different groups in receiving important information. Furthermore, in many of these applications, the spread of influence is time-critical, i.e., it is only beneficial to be influenced before a time deadline. As we show in this paper, the time-criticality of the information could further exacerbate the disparity of influence across groups. This disparity, introduced by algorithms aimed at maximizing total influence, could have far-reaching consequences, impacting people's prosperity and putting minority groups at a big disadvantage. In this work, we propose a notion of group fairness in time-critical influence maximization. We introduce surrogate objective functions to solve the influence maximization problem under fairness considerations. By exploiting the submodularity structure of our objectives, we provide computationally efficient algorithms with guarantees that are effective in enforcing fairness during the propagation process. We demonstrate the effectiveness of our approach through synthetic and real-world experiments.
  Online social networks are now a popular way for users to connect, express themselves, and share content. Users in today's online social networks often post a profile, consisting of attributes like geographic location, interests, and schools attended. Such profile information is used on the sites as a basis for grouping users, for sharing content, and for suggesting users who may benefit from interaction. However, in practice, not all users provide these attributes. In this paper, we ask the question: given attributes for some fraction of the users in an online social network, can we infer the attributes of the remaining users? In other words, can the attributes of users, in combination with the social network graph, be used to predict the attributes of another user in the network? To answer this question, we gather fine-grained data from two social networks and try to infer user profile attributes. We find that users with common attributes are more likely to be friends and often form dense communities, and we propose a method of inferring user attributes that is inspired by previous approaches to detecting communities in social networks. Our results show that certain user attributes can be inferred with high accuracy when given information on as little as 20 of the users. In this work, we study the notion of competing campaigns in a social network and address the problem of influence limitation where a "bad" campaign starts propagating from a certain node in the network and use the notion of limiting campaigns to counteract the effect of misinformation. The problem can be summarized as identifying a subset of individuals that need to be convinced to adopt the competing (or "good") campaign so as to minimize the number of people that adopt the "bad" campaign at the end of both propagation processes. We show that this optimization problem is NP-hard and provide approximation guarantees for a greedy solution for various definitions of this problem by proving that they are submodular. We experimentally compare the performance of the greedy method to various heuristics. The experiments reveal that in most cases inexpensive heuristics such as degree centrality compare well with the greedy approach. We also study the influence limitation problem in the presence of missing data where the current states of nodes in the network are only known with a certain probability and show that prediction in this setting is a supermodular problem. We propose a prediction algorithm that is based on generating random spanning trees and evaluate the performance of this approach. The experiments reveal that using the prediction algorithm, we are able to tolerate about 90 missing data before the performance of the algorithm starts degrading and even with large amounts of missing data the performance degrades only to 75 of the performance that would be achieved with complete data. Models for the processes by which ideas and influence propagate through a social network have been studied in a number of domains, including the diffusion of medical and technological innovations, the sudden and widespread adoption of various strategies in game-theoretic settings, and the effects of "word of mouth" in the promotion of new products. Recently, motivated by the design of viral marketing strategies, Domingos and Richardson posed a fundamental algorithmic problem for such social network processes: if we can try to convince a subset of individuals to adopt a new product or innovation, and the goal is to trigger a large cascade of further adoptions, which set of individuals should we target?We consider this problem in several of the most widely studied models in social network analysis. The optimization problem of selecting the most influential nodes is NP-hard here, and we provide the first provable approximation guarantees for efficient algorithms. Using an analysis framework based on submodular functions, we show that a natural greedy strategy obtains a solution that is provably within 63 of optimal for several classes of models; our framework suggests a general approach for reasoning about the performance guarantees of algorithms for these types of influence problems in social networks.We also provide computational experiments on large collaboration networks, showing that in addition to their provable guarantees, our approximation algorithms significantly out-perform node-selection heuristics based on the well-studied notions of degree centrality and distance centrality from the field of social networks. This paper proposes an alternative way to identify nodes with high betweenness centrality. It introduces a new metric, κ-path centrality, and a randomized algorithm for estimating it, and shows empirically that nodes with high κ-path centrality have high node betweenness centrality. The randomized algorithm runs in time O(κ3n2−2αlog n) and outputs, for each vertex v, an estimate of its κ-path centrality up to additive error of ±n1 2+α with probability 1 − 1 n2. Experimental evaluations on real and synthetic social networks show improved accuracy in detecting high betweenness centrality nodes and significantly reduced execution time when compared with existing randomized algorithms. Social networks often serve as a medium for the diffusion of ideas or innovations. An individual's decision whether to adopt a product or innovation will be highly dependent on the choices made by the individual's peers or neighbors in the social network. In this work, we study the game of innovation diffusion with multiple competing innovations such as when multiple companies market competing products using viral marketing. Our first contribution is a natural and mathematically tractable model for the diffusion of multiple innovations in a network. We give a (1-1 e) approximation algorithm for computing the best response to an opponent's strategy, and prove that the "price of competition" of this game is at most 2. We also discuss "first mover" strategies which try to maximize the expected diffusion against perfect competition. Finally, we give an FPTAS for the problem of maximizing the influence of a single player when the underlying graph is a tree. We consider the problem faced by a company that wants to use viral marketing to introduce a new product into a market where a competing product is already being introduced. We assume that consumers will use only one of the two products and will influence their friends in their decision of which product to use. We propose two models for the spread of influence of competing technologies through a social network and consider the influence maximization problem from the follower's perspective. In particular we assume the follower has a fixed budget available that can be used to target a subset of consumers and show that, although it is NP-hard to select the most influential subset to target, it is possible to give an efficient algorithm that is within 63 of optimal. Our computational experiments show that by using knowledge of the social network and the set of consumers targeted by the competitor, the follower may in fact capture a majority of the market by targeting a relatively small set of the right consumers.