Ramasuri Narayanam

A Shapley Value-Based Approach to Discover Influential Nodes in Social Networks

Our study concerns an important current problem, that of diffusion of information in social networks. This problem has received significant attention from the Internet research community in the recent times, driven by many potential applications such as viral marketing and sales promotions. In this paper, we focus on the target set selection problem, which involves discovering a small subset of influential players in a given social network, to perform a certain task of information diffusion. The target set selection problem manifests in two forms: 1) top-k nodes problem and 2) λ -coverage problem. In the top-k nodes problem, we are required to find a set of k key nodes that would maximize the number of nodes being influenced in the network. The λ-coverage problem is concerned with finding a set of key nodes having minimal size that can influence a given percentage λ of the nodes in the entire network. We propose a new way of solving these problems using the concept of Shapley value which is a well known solution concept in cooperative game theory. Our approach leads to algorithms which we call the ShaPley value-based Influential Nodes (SPINs) algorithms for solving the top-k nodes problem and the λ -coverage problem. We compare the performance of the proposed SPIN algorithms with well known algorithms in the literature. Through extensive experimentation on four synthetically generated random graphs and six real-world data sets (Celegans, Jazz, NIPS coauthorship data set, Netscience data set, High-Energy Physics data set, and Political Books data set), we show that the proposed SPIN approach is more powerful and computationally efficient.

Topologies of Strategically Formed Social Networks Based on a Generic Value Function - Allocation Rule Model

Abstract A wide variety of game theoretic models have been proposed in the literature to explain social network formation. Topologies of networks formed under these models have been investigated, keeping in view two key properties, namely efficiency and stability. Our objective in this paper is to investigate the topologies of networks formed with a more generic model of network formation. Our model is based on a well known model, the value function – allocation rule model. We choose a specific value function and a generic allocation rule and derive several interesting topological results in the network formation context. A unique feature of our model is that it simultaneously captures several key determinants of network formation such as (i) benefits from immediate neighbors through links, (ii) costs of maintaining the links, (iii) benefits from non-neighboring nodes and decay of these benefits with distance, and (iv) intermediary benefits that arise from multi-step paths. Based on this versatile model of network formation, our study explores the structure of the networks that satisfy one or both of the properties, efficiency and pairwise stability. The following are our specific results: (1) we first show that the complete graph and the star graph are the only topologies possible for non-empty efficient networks; this result is independent of the allocation rule and corroborates the findings of more specific models in the literature. (2) We then derive the structure of pairwise stable networks and come up with topologies that are richer than what have been derived for extant models in the literature. (3) Next, under the proposed model, we state and prove a necessary and sufficient condition for any efficient network to be pairwise stable. (4) Finally, we study topologies of pairwise stable networks in some specific settings, leading to unravelling of more specific topological possibilities.

A shapley value-based approach to determine gatekeepers in social networks with applications

Inspired by emerging applications of social networks, we introduce in this paper a new centrality measure termed gatekeeper centrality. The new centrality is based on the well-known game-theoretic concept of Shapley value and, as we demonstrate, possesses unique qualities compared to the existing metrics. Furthermore, we present a dedicated approximate algorithm, based on the Monte Carlo sampling method, to compute the gatekeeper centrality. We also consider two well known applications in social network analysis, namely community detection and limiting the spread of mis-information; and show the merit of using the proposed framework to solve these two problems in comparison with the respective benchmark algorithms.

Viral marketing for product cross-sell through social networks

The well known influence maximization problem [1] (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. In this paper, we introduce a novel and generalized version of the influence maximization problem that considers simultaneously the following three practical aspects: (i) Often cross-sell among products is possible, (ii) Product specific costs (and benefits) for promoting the products have to be considered, and (iii) Since a company often has budget constraints, the initial seeds have to be chosen within a given budget. We refer to this generalized problem setting as Budgeted Influence Maximization with Cross-sell of Products (B-IMCP). To the best of our knowledge, we are not aware of any work in the literature that addresses the B-IMCP problem which is the subject matter of this paper. Given a fixed budget, one of the key issues associated with the B-IMCP problem is to choose the initial seeds within this budget not only for the individual products, but also for promoting cross-sell phenomenon among these products. In particular, the following are the specific contributions of this paper: (i) We propose an influence propagation model to capture both the cross-sell phenomenon and product specific costs and benefits; (ii) As the B-IMCP problem is NP-hard computationally, we present a simple greedy approximation algorithm and then derive the approximation guarantee of this greedy algorithm by drawing upon the results from the theory of matroids; (iii) We then outline two efficient heuristics based on well known concepts in the literature. Finally, we experimentally evaluate the proposed approach for the B-IMCP problem using a few well known social network data sets such as WikiVote data set, Epinions, and Telecom call detail records data.

DiSCern: A diversified citation recommendation system for scientific queries

Performing literature survey for scholarly activities has become a challenging and time consuming task due to the rapid growth in the number of scientific articles. Thus, automatic recommendation of high quality citations for a given scientific query topic is immensely valuable. The state-of-the-art on the problem of citation recommendation suffers with the following three limitations. First, most of the existing approaches for citation recommendation require input in the form of either the full article or a seed set of citations, or both. Nevertheless, obtaining the recommendation for citations given a set of keywords is extremely useful for many scientific purposes. Second, the existing techniques for citation recommendation aim at suggesting prestigious and well-cited articles. However, we often need recommendation of diversified citations of the given query topic for many scientific purposes; for instance, it helps authors to write survey papers on a topic and it helps scholars to get a broad view of key problems on a topic. Third, one of the problems in the keyword based citation recommendation is that the search results typically would not include the semantically correlated articles if these articles do not use exactly the same keywords. To the best of our knowledge, there is no known citation recommendation system in the literature that addresses the above three limitations simultaneously. In this paper, we propose a novel citation recommendation system called DiSCern to precisely address the above research gap. DiSCern finds relevant and diversified citations in response to a search query, in terms of keyword(s) to describe the query topic, while using only the citation graph and the keywords associated with the articles, and no latent information. We use a novel keyword expansion step, inspired by community finding in social network analysis, in DiSCern to ensure that the semantically correlated articles are also included in the results. Our proposed approach primarily builds on the Vertex Reinforced Random Walk (VRRW) to balance prestige and diversity in the recommended citations. We demonstrate the efficacy of DiSCern empirically on two datasets: a large publication dataset of more than 1.7 million articles in computer science domain and a dataset of more than 29,000 articles in theoretical high-energy physics domain. The experimental results show that our proposed approach is quite efficient and it outperforms the state-of-the-art algorithms in terms of both relevance and diversity.

Game theoretic models for social network analysis

The existing methods and techniques for social network analysis are inadequate to capture both the behavior (such as rationality and intelligence) of individuals and the strategic interactions that occur among these individuals. Game theory is a natural tool to overcome this inadequacy since it provides rigorous mathematical models of strategic interaction among autonomous, intelligent, and rational agents. Motivated by the above observation, this tutorial provides the conceptual underpinnings of the use of game theoretic models in social network analysis. In the first part of the tutorial, we provide rigorous foundations of relevant concepts in game theory and social network analysis. In the second part of the tutorial, we present a comprehensive study of four contemporary and pertinent problems in social networks: social network formation, determining in influential individuals for viral marketing, query incentive networks, and community detection.

Design of viral marketing strategies for product cross-sell through social networks

In this paper, we introduce a novel and generalized version of the influence maximization problem in social networks, which we call as Budgeted Influence Maximization with Cross-sell of Products (B-IMCP), and it considers simultaneously the following three practical aspects: (i) Often cross-sell among products is possible, (ii) Product-specific costs (and benefits) for promoting the products have to be considered, and (iii) Since a company often has budget constraints, the initial seeds have to be chosen within a given budget. In particular, we consider that the cross-sell relationships among the products of a single company are given by an arbitrary bipartite graph. We explore two variants of cross-sell, one weak and one strong, and also assume product-specific costs and benefits. This leads to two different versions of the B-IMCP problem. Given a fixed budget, one of the key issues associated with each version of the B-IMCP problem is to choose the initial seeds within this budget not only for the individual products, but also for promoting cross-sell phenomenon among these products. The following are the specific contributions of this paper: (i) We propose a novel influence propagation model to capture both the cross-sell phenomenon and the costs–benefits for the products; (ii) For each version of the B-IMCP problem, we note that the problem turns out to be NP-hard, and then, we present a simple greedy approximation algorithm for the same. We derive the approximation ratio of this greedy algorithm by drawing upon certain key results from the theory of matroids; (iii) We then outline three heuristics based on well-known concepts from the sociology literature; and (iv) Finally, we experimentally compare and contrast the proposed algorithms and heuristics using certain well-known social network data sets such as WikiVote trust network, Epinions, and Telco call detail records data. Based on the experiments, we consistently found that the stronger the cross-sell relationship between the products, the larger the overlap between the seeds of these products and lesser the distances among the corresponding non-overlapping seeds.

A Novel and Model Independent Approach for Efficient Influence Maximization in Social Networks

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.

Bug resolution catalysts: Identifying essential non-committers from bug repositories

Bugs are inevitable in software projects. Resolving bugs is the primary activity in software maintenance. Developers, who fix bugs through code changes, are naturally important participants in bug resolution. However, there are other participants in these projects who do not perform any code commits. They can be reporters reporting bugs; people having a deep technical know-how of the software and providing valuable insights on how to solve the bug; bug-tossers who re-assign the bugs to the right set of developers. Even though all of them act on the bugs by tossing and commenting, not all of them may be crucial for bug resolution. In this paper, we formally define essential non-committers and try to identify these bug resolution catalysts. We empirically study 98304 bug reports across 11 open source and 5 commercial software projects for validating the existence of such catalysts. We propose a network analysis based approach to construct a Minimal Essential Graph that identifies such people in a project. Finally, we suggest ways of leveraging this information for bug triaging and bug report summarization.

A Game Theoretic Approach to Identify Critical Components in Networked Systems

Networked systems are pervasive in the current Internet age and they manifest in several ways such as online and enterprize social networks, data center networks, cloud service networks, and global business networks. Such networked systems generally consist of entities and connections (or edges) among these entities. As services or applications are deployed over these networks, the success of any service or application is crucially dependent on the high availability of the components (namely, entities and connections) in the network. This calls for an important problem of identifying the critical components in the network to improve the quality of the services offered over these networks. We propose a novel and generic game theoretic framework to identify critical components with respect to a given task (or service or application) in the network. In particular, we apply the proposed generic game theoretic framework to determine critical edges in the context of k-edge connectivity between certain pairs of nodes in a given network. We call a pair of nodes in a network k-edge connected if there exists k-edge disjoint (shortest) paths between these nodes. Identifying critical edges in the setting of the k-edge connectivity is an extremely important problem especially in the context of data center networks and cloud service networks. The following are the specific contributions of this paper: (1) We first formally define a game theoretic model for the k-edge connectivity between certain pairs of nodes in the network. We refer to this as k-edge connectivity game. We then define the criticality of any edge to be the value of its Banzhaf power index in the k-edge connectivity game. In this setting, identifying critical edges boils down to the computation of Banzhaf power index in the k-edge connectivity game; (2) We then show that computing the Banzhaf power index for any edge in the k-edge connectivity game is #P-complete. We show this result by reducing the problem of counting the number of perfect matchings in a given graph to an instance of computing the Banzhaf power index for an edge in the k-edge connectivity game. This implies that the computation of Banzhaf power index for an edge in the k-edge connectivity game is computationally hard; (3) To alleviate this computational issue, we propose an approximation algorithm and also we present a simple heuristic based on the notion of Shapley value in cooperative game theory; (4) We then derive a closed form expression for computing the Banzhaf power index of any edge in the k-edge connectivity game, when the network structure is a tree; and (5) We finally evaluate the proposed approach using thorough experimentation on certain real world network data sets.