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Approximate nearest neighbor search (ANNS) is a fundamental problem indatabases and data mining. A scalable ANNS algorithm should be bothmemory-efficient and fast. Some early graph-based approaches have shownattractive theoretical guarantees on search time complexity, but they allsuffer from the problem of high indexing time complexity. Recently, somegraph-based methods have been proposed to reduce indexing complexity byapproximating the traditional graphs; these methods have achieved revolutionaryperformance on million-scale datasets. Yet, they still can not scale tobillion-node databases. In this paper, to further improve the search-efficiencyand scalability of graph-based methods, we start by introducing four aspects:(1) ensuring the connectivity of the graph; (2) lowering the average out-degreeof the graph for fast traversal; (3) shortening the search path; and (4)reducing the index size. Then, we propose a novel graph structure calledMonotonic Relative Neighborhood Graph (MRNG) which guarantees very low searchcomplexity (close to logarithmic time). To further lower the indexingcomplexity and make it practical for billion-node ANNS problems, we propose anovel graph structure named Navigating Spreading-out Graph (NSG) byapproximating the MRNG. The NSG takes the four aspects into accountsimultaneously. Extensive experiments show that NSG outperforms all theexisting algorithms significantly. In addition, NSG shows superior performancein the E-commercial search scenario of Taobao (Alibaba Group) and has beenintegrated into their search engine at billion-node scale.

Fast Approximate Nearest Neighbor Search With The Navigating Spreading-out Graph