On Adaptivity Gaps of Influence Maximization Under the Independent Cascade Model with Full-Adoption Feedback

In this paper, we study the adaptivity gap of the influence maximization problem under the independent cascade model when full-adoption feedback is available. Our main results are to derive upper bounds on several families of well-studied influence graphs, including in-arborescences, out-arborescences and bipartite graphs. Especially, we prove that the adaptivity gap for the in-arborescences is between [e/(e-1), 2e/(e-1)], and for the out-arborescences the gap is between [e/(e-1), 2]. These are the first constant upper bounds in the full-adoption feedback model. Our analysis provides several novel ideas to tackle the correlated feedback appearing in adaptive stochastic optimization, which may be of independent interest

Continuous Influence-based Community Partition for Social Networks

Community partition is of great importance in social networks because of the rapid increasing network scale, data and applications. We consider the community partition problem under LT model in social networks, which is a combinatorial optimization problem that divides the social network to disjoint $m$ communities. Our goal is to maximize the sum of influence propagation through maximizing it within each community. As the influence propagation function of community partition problem is supermodular under LT model, we use the method of Lov{$\acute{a}$}sz Extension to relax the target influence function and transfer our goal to maximize the relaxed function over a matroid polytope. Next, we propose a continuous greedy algorithm using the properties of the relaxed function to solve our problem, which needs to be discretized in concrete implementation. Then, random rounding technique is used to convert the fractional solution to integer solution. We present a theoretical analysis with $1-1/e$ approximation ratio for the proposed algorithms. Extensive experiments are conducted to evaluate the performance of the proposed continuous greedy algorithms on real-world online social networks datasets and the results demonstrate that continuous community partition method can improve influence spread and accuracy of the community partition effectively.Comment: arXiv admin note: text overlap with arXiv:2003.1043

Graph Algorithms and Applications

The mixture of data in real-life exhibits structure or connection property in nature. Typical data include biological data, communication network data, image data, etc. Graphs provide a natural way to represent and analyze these types of data and their relationships. Unfortunately, the related algorithms usually suffer from high computational complexity, since some of these problems are NP-hard. Therefore, in recent years, many graph models and optimization algorithms have been proposed to achieve a better balance between efficacy and efficiency. This book contains some papers reporting recent achievements regarding graph models, algorithms, and applications to problems in the real world, with some focus on optimization and computational complexity

Complexity, Algorithms, and Heuristics of Influence Maximization

People often adopt improved behaviors, products, or ideas through the influence of friends. This is modeled by emph{cascades}. One way to spread such positive elements through society is to identify those most influential agents---those that cause the maximum spread, and initiate the spread by seeding them. However, this strategy has a key difficulty: finding these influential seed nodes. This is difficult even if both the network structure and the way the cascade spreads are known. In emph{the influence maximization problem}, a central planner is given a graph and a limited budget $k$, and he needs to pick $k$ seeds such that the expected total number of infected vertices in the graph at the end of the cascade is maximized. This problem plays a central role in viral marketing, outbreak detection, rumor controls, etc. This thesis focuses on computational complexity, approximability and algorithm/heuristic design aspects of the influence maximization problem, with both emph{submodular} and emph{nonsubmodular} diffusion models. The first part of the thesis studies submodular influence maximization mainly in the computational complexity and algorithm analysis aspects, which includes some breakthroughs in understanding the approximability of submodular influence maximization and the theoretical performance of the well-studied greedy algorithm. The second part of the thesis focuses on nonsubmodular influence maximization. New sociologically founded nonsubmodular diffusion models are proposed, and we show how the seeding strategy for nonsubmodular diffusion models is fundamentally different compared to submodular diffusion models.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155221/1/bstao_1.pd