Graph-based approaches to nearest neighbor search are popular and powerful tools for handling large datasets in practice, but they have limited theoretical guarantees. We study the worst-case performance of recent graph-based approximate nearest neighbor search algorithms, such as HNSW, NSG and DiskANN. For DiskANN, we show that its "slow preprocessing" version provably supports approximate nearest neighbor search query with constant approximation ratio and poly-logarithmic query time, on data sets with bounded "intrinsic" dimension. For the other data structure variants studied, including DiskANN with "fast preprocessing", HNSW and NSG, we present a family of instances on which the empirical query time required to achieve a "reasonable" accuracy is linear in instance size. For example, for DiskANN, we show that the query procedure can take at least $0.1 n$ steps on instances of size $n$ before it encounters any of the $5$ nearest neighbors of the query.

图形化相似最近邻搜索算法的最坏情况性能研究，以HNSW、NSG和DiskANN为例，发现其实际查询时间与实例大小成线性关系，并证明其具有常数近似比和多对数查询时间的边界维数据集。

流行近似最近邻搜索实现的最坏情况性能：保证和限制