Match each vector index type to its primary characteristic.

Vector indexes solve the 'find K nearest neighbors of this query vector' problem at scale. The four names in this question are the families and tools you will see in every modern vector database. **Flat** is brute force. Compute the distance from the query to every vector in the database, return the top K. Exact, no recall loss, but `O(N)` per query. Above 100k vectors it stops being viable for interactive latency. **HNSW** (Hierarchical Navigable Small World) is a graph index. Each vector is linked to a few neighbors in a small-world graph; search hops along the edges. Excellent recall, sub millisecond latency, but the graph eats 2 to 4 times the raw vector storage. **IVF** (Inverted File) partitions vectors into k-means clusters. At query time it only scans the closest few clusters (controlled by `nprobe`). Cheaper than HNSW on memory, slower per query, lower recall at the same compute. **PQ** (Product Quantization) is a compression scheme, not a search index. It chops each vector into subvectors and quantizes each one to a few bytes via a learned codebook. Composed with IVF as `IVF-PQ`, it shrinks billion vector indexes to single machine RAM.

**Four pieces, three families and a compression layer.** `HNSW` is a graph based index. Hierarchical small-world graph, sub millisecond latency, recall above 0.99 at the cost of 2 to 4 times memory overhead. The default for sub 100M vector deployments in Pinecone, Weaviate, and Qdrant. `IVF` is a partition based index. K-means clusters the vectors; queries probe only the closest few clusters. Memory overhead is small, recall is lower at the same compute, latency is higher. Almost always composed with PQ for production deployments. `Flat` is exact brute force. No index structure, just dense distance computation against every vector. Useful as a recall baseline and for tiny corpora (under 100k vectors) where indexing overhead is not worth it. `PQ` is not an index family. It is a vector compression scheme that splits each vector into `pq_m` subvectors. Each subvector is quantized to 8 bits via a learned codebook. Per vector memory drops from kilobytes to tens of bytes. It composes with IVF (`IVF-PQ`) or HNSW, never used alone for search. The pairs in the question reflect this: HNSW-graph, IVF-partition, Flat-exact, PQ-compress.