Approximate nearest neighbor search (ANNS) is a fundamental problem in databases and data mining. A scalable ANNS algorithm should be both memory-efficient and fast. Some early graph-based approaches have shown attractive theoretical guarantees on search time complexity, but they all suffer from the problem of high indexing time complexity. Recently, some graph-based methods have been proposed to reduce indexing complexity by approximating the traditional graphs; these methods have achieved revolutionary performance on million-scale datasets. Yet, they still can not scale to billion-node databases. In this paper, to further improve the search-efficiency and scalability of graph-based methods, we start by introducing four aspects: (1) ensuring the connectivity of the graph; (2) lowering the average out-degree of the graph for fast traversal; (3) shortening the search path; and (4) reducing the index size. Then, we propose a novel graph structure called Monotonic Relative Neighborhood Graph (MRNG) which guarantees very low search complexity (close to logarithmic time). To further lower the indexing complexity and make it practical for billion-node ANNS problems, we propose a novel graph structure named Navigating Spreading-out Graph (NSG) by approximating the MRNG. The NSG takes the four aspects into account simultaneously. Extensive experiments show that NSG outperforms all the existing algorithms significantly. In addition, NSG shows superior performance in the E-commercial search scenario of Taobao (Alibaba Group) and has been integrated into their search engine at billion-node scale.

Automatic modulation classification enables intelligent communications and it is of crucial importance in today's and future wireless communication networks. Although many automatic modulation classification schemes have been proposed, they cannot tackle the intra-class diversity problem caused by the dynamic changes of the wireless communication environment. In order to overcome this problem, inspired by face recognition, a novel automatic modulation classification scheme is proposed by using the multi-scale network in this paper. Moreover, a novel loss function that combines the center loss and the cross entropy loss is exploited to learn both discriminative and separable features in order to further improve the classification performance. Extensive simulation results demonstrate that our proposed automatic modulation classification scheme can achieve better performance than the benchmark schemes in terms of the classification accuracy. The influence of the network parameters and the loss function with the two-stage training strategy on the classification accuracy of our proposed scheme are investigated. H. Zhang, F. Zhou, and Qihui Wu are with College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106 China. They are also with Key Laboratory of Dynamic Cognitive System of Electromagnetic Spectrum Space (Nanjing University of Aeronautics and Astronautics), and with Ministry of Industry and Information Technology, Nanjing, 211106, China (email: haozhangcn@nuaa.edu.cn, W. Wu is with the Nanjing University of Posts and Telecommunications, Nanjing 210003, China, also with the Key Laboratory of Dynamic Cognitive System of Electromagnetic Spectrum Space, Ministry of Industry and Information Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China (e-mail: weiwu@njupt.edu.cn). R. Q. Hu is with the Department of Electrical and Computer Engineering, Utah State University, Logan, UT 84322 USA (e-mail: rosehu@ieee.org). ITH the commercial applications of the fifth generation (5G) wireless communication networks, the sixth generation (6G) wireless communication networks have received an increasing attention from both academia and industry [1] and [2]. Intelligent communication empowered by artificial intelligence is one of the most evident characteristics of 6G wireless communication systems. To realize this goal, it is of crucial importance to automatically recognize the modulation types [3].