Searching through massive collections of high-dimensional vectors to find the exact nearest neighbors can be computationally expensive, often too slow for interactive applications. When dealing with the scale encountered in vector databases, performing an exhaustive search for every query is usually impractical.

This chapter addresses this challenge by introducing Approximate Nearest Neighbor (ANN) search. You will learn why approximation is often necessary and how ANN algorithms provide a practical solution by trading a small degree of accuracy for substantial improvements in search speed and resource usage.

We will cover:

• The computational limits of exact nearest neighbor search in high dimensions.
• The core concepts of ANN, particularly the trade-off between search recall and performance metrics like latency.
• An overview of common ANN algorithms, including Hierarchical Navigable Small Worlds (HNSW), Inverted File Index (IVF), and Locality-Sensitive Hashing (LSH), explaining how each works.
• Key parameters used to build and tune ANN indexes (e.g., $ef\_construction$, $ef\_search$, $nlist$, $m$) and their impact.
• Methods for evaluating the effectiveness and efficiency of ANN indexes using relevant metrics.

The chapter concludes with a hands-on practical session where you will experiment with building different ANN indexes and observe the resulting performance characteristics.