Search

Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet economics and multi-agent learning. This paper reviews various algorithms computing the Nash equilibrium and its approximation solutions in finite normal-form games from both theoretical and empirical perspectives. For the theoretical part, we classify algorithms in the literature and present basic ideas on algorithm design and analysis. For the empirical part, we present a comprehensive comparison on the algorithms in the literature over different kinds of games. Based on these results, we provide practical suggestions on implementations and uses of these algorithms. Finally, we present a series of open problems from both theoretical and practical considerations. • A classification on Nash equilibrium algorithms in the literature with basic ideas on design and analysis presented. • A comprehensive comparison on Nash equilibrium algorithms in the literature over different kinds of games. • Practical suggestions on implementations and uses of Nash equilibrium algorithms. [ABSTRACT FROM AUTHOR]

Clustering is an essential tool in data mining research and applications. It is the subject of active research in many fields of study, such as computer science, data science, statistics, pattern recognition, artificial intelligence, and machine learning. Several clustering techniques have been proposed and implemented, and most of them successfully find excellent quality or optimal clustering results in the domains mentioned earlier. However, there has been a gradual shift in the choice of clustering methods among domain experts and practitioners alike, which is precipitated by the fact that most traditional clustering algorithms still depend on the number of clusters provided a priori. These conventional clustering algorithms cannot effectively handle real-world data clustering analysis problems where the number of clusters in data objects cannot be easily identified. Also, they cannot effectively manage problems where the optimal number of clusters for a high-dimensional dataset cannot be easily determined. Therefore, there is a need for improved, flexible, and efficient clustering techniques. Recently, a variety of efficient clustering algorithms have been proposed in the literature, and these algorithms produced good results when evaluated on real-world clustering problems. This study presents an up-to-date systematic and comprehensive review of traditional and state-of-the-art clustering techniques for different domains. This survey considers clustering from a more practical perspective. It shows the outstanding role of clustering in various disciplines, such as education, marketing, medicine, biology, and bioinformatics. It also discusses the application of clustering to different fields attracting intensive efforts among the scientific community, such as big data, artificial intelligence, and robotics. This survey paper will be beneficial for both practitioners and researchers. It will serve as a good reference point for researchers and practitioners to design improved and efficient state-of-the-art clustering algorithms. • Provide an up-to-date comprehensive review of the different clustering techniques. • Highlight novel and most recent practical applications areas of clustering. • Provide a convenient research path for new researchers. • Help experts develop new algorithms for emerging challenges in the research area. [ABSTRACT FROM AUTHOR]

The shortest path problem, one of the most classical graph problems, has been addressed in many different ways suitable for various settings in the fields of computer science and artificial intelligence. In this paper, we revisit a distributed control solution, namely the continuous-time adaptive Bellman–Ford algorithm, to the shortest path problem. While previous work only concerned its global asymptotic stability, we not only prove its global asymptotic stability by formulating a Lyapunov function, but characterize the initial conditions under which the algorithm will converge exponentially, and show that the algorithm is globally ultimately bounded under persistent bounded perturbations based on the proposed Lyapunov function. [ABSTRACT FROM AUTHOR]