  Approximate nearest neighbor search (ANNS) constitutes an important operation
in a multitude of applications, including recommendation systems, information
retrieval, and pattern recognition. In the past decade, graph-based ANNS
algorithms have been the leading paradigm in this domain, with dozens of
graph-based ANNS algorithms proposed. Such algorithms aim to provide effective,
efficient solutions for retrieving the nearest neighbors for a given query.
Nevertheless, these efforts focus on developing and optimizing algorithms with
different approaches, so there is a real need for a comprehensive survey about
the approaches' relative performance, strengths, and pitfalls. Thus here we
provide a thorough comparative analysis and experimental evaluation of 13
representative graph-based ANNS algorithms via a new taxonomy and fine-grained
pipeline. We compared each algorithm in a uniform test environment on eight
real-world datasets and 12 synthetic datasets with varying sizes and
characteristics. Our study yields novel discoveries, offerings several useful
principles to improve algorithms. This effort also helped us pinpoint
algorithms' working portions, along with rule-of-thumb recommendations about
promising research directions and suitable algorithms for practitioners in
different fields.
