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"abstract": "<italic>k</italic>-nearest neighbor graph is a fundamental data structure in many disciplines such as information retrieval, data-mining, pattern recognition, and machine learning, etc. In the literature, considerable research has been focusing on how to efficiently build an approximate <italic>k</italic>-nearest neighbor graph (<italic>k</italic>-NN graph) for a fixed dataset. Unfortunately, a closely related issue of how to merge two existing <italic>k</italic>-NN graphs has been overlooked. In this paper, we address the issue of <italic>k</italic>-NN graph merging in two different scenarios. In the first scenario, a symmetric merge algorithm is proposed to combine two approximate <italic>k</italic>-NN graphs. The algorithm facilitates large-scale processing by the efficient merging of <italic>k</italic>-NN graphs that are produced in parallel. In the second scenario, a joint merge algorithm is proposed to expand an existing <italic>k</italic>-NN graph with a raw dataset. The algorithm enables the incremental construction of a hierarchical approximate <italic>k</italic>-NN graph. Superior performance is attained when leveraging the hierarchy for NN search of various data types, dimensionality, and distance measures.",
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