We present a theoretical and empirical analysis of the adaptive entry point selection for graph-based approximate nearest neighbor search (ANNS). We introduce novel concepts: $b\textit{-monotonic path}$ and $B\textit{-MSNET}$, which better capture an actual graph in practical algorithms than existing concepts like MSNET. We prove that adaptive entry point selection offers better performance upper bound than the fixed central entry point under more general conditions than previous work. Empirically, we validate the method's effectiveness in accuracy, speed, and memory usage across various datasets, especially in challenging scenarios with out-of-distribution data and hard instances. Our comprehensive study provides deeper insights into optimizing entry points for graph-based ANNS for real-world high-dimensional data applications.

翻译：我们针对基于图结构的近似最近邻搜索（ANNS）中的自适应入口点选择进行了理论与实证分析。我们引入了新概念：$b\textit{-单调路径}$与$B\textit{-MSNET}$。与现有概念（如MSNET）相比，这些概念能更准确地描述实际算法中的图结构。我们证明了在比先前工作更一般的条件下，自适应入口点选择比固定中心入口点具有更优的性能上限。实验方面，我们在多个数据集上验证了该方法在精度、速度和内存使用方面的有效性，尤其是在处理分布外数据与困难实例等具有挑战性的场景中。本综合研究为优化基于图结构的ANNS中面向真实高维数据应用的入口点选择提供了更深入的洞见。