发表机构
CICESE（墨西哥西南科学研究与高等教育中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究测量了基于搜索的图构建中批处理与增量构建的性能差异，发现自适应距离评估导致的随机访问瓶颈是主要限制，并提出双上限屋顶线模型来界定其影响。
AI 中文摘要
用于最近邻搜索的可导航图要么增量构建，即每个插入点在一个随构建过程而变化的图中进行搜索，要么在固定基底上批量构建，后者以构建时间为代价换来了确定性和并行性。我们测量了这一代价并找出其来源。在一台64线程机器上，我们对调优后的Vamana和PiPNN进行性能剖析，并以配对设计重复构建每个系统，将构建时间分解为工作量（距离评估次数）和每次评估的成本。让批量构建器的基底在$B$个同步块中变化，可以恢复增量构建的反馈循环，同时图仍然是（数据、种子、参数、$B$）的函数：八棵具有批处理反馈的树匹配三十二棵冻结树，并且构建完成了Vamana距离工作量的$0.88\times$。然而，它花费了Vamana墙钟时间的$1.55\times$，因为变化的基底每次评估成本更高。进一步推进，我们发现了一个任何基于搜索的构建器都无法跨越的瓶颈。它们中的每一个，无论是增量还是批处理，都自适应地评估距离，一次一个依赖的随机访问，在同一台机器上，在$d \thickapprox 100$时，其运行速度比密集内核低$20$-$27\times$，当数据驻留在缓存中时，低五到六倍。这一差距并非低维伪影：自适应评估成本为$d^{1.04}$，而分块评估成本为$d^{0.63}$，因此瓶颈随$d^{0.4}$增长，在$d = 960$时比在$d = 128$时高一倍。PiPNN的数量级构建优势在于该内核：它评估每个点的距离数量相同，但以预先固定的密集块进行评估。我们表明，波束不能事后批处理（同步块的有用密度为2-3%），将瓶颈表述为双上限的屋顶线，并界定其范围：每当距离是黑盒或评估顺序依赖于数据时，该瓶颈就会生效。
英文摘要
Navigable graphs for nearest-neighbor search are built either incrementally, each inserted point searching a graph that mutates as construction proceeds, or in batch over a fixed substrate, which buys determinism and parallelism at a price in build time. We measure that price and find where it comes from. Instrumenting a tuned Vamana and PiPNN and building every system repeatedly in a paired design on one 64-thread machine, we separate build time into work (distance evaluations) and cost per evaluation. Letting the batch builder's substrate mutate in $B$ synchronous blocks recovers the feedback loop of incremental construction while the graph stays a function of (data, seed, parameters, $B$): eight trees with batched feedback match thirty-two frozen trees, and the build does $0.88\times$ Vamana's distance work. Yet it takes $1.55\times$ Vamana's wall-clock, because the mutating substrate costs more per evaluation. Pushing further, we find a wall that no search-based builder crosses. Every one of them, incremental or batched, evaluates distances adaptively, one dependent random access at a time, and runs $20$-$27\times$ below a dense kernel on the same machine at $d \approx 100$, five to six times of it with the data resident in cache. The gap is not a low-dimension artifact: an adaptive evaluation costs $d^{1.04}$ and a blocked one $d^{0.63}$, so the wall grows as $d^{0.4}$ and is twice as high at $d = 960$ as at $d = 128$. PiPNN's order-of-magnitude build advantage is that kernel: it evaluates as many distances per point, but as fixed-in-advance dense blocks. We show the beam cannot be batched after the fact (the useful density of a lockstep block is 2-3%), state the wall as a two-ceiling roofline, and delimit it: it binds whenever the distance is a black box or the evaluation order is data-dependent.
