What happens to index build time and query performance as the number of vectors grows from 1 million to 1 billion? What scaling behaviors (linear, sublinear, etc.) are expected or observed?

When scaling a vector index from 1 million to 1 billion vectors, both index build time and query performance are impacted, with behaviors varying based on the algorithm and implementation. Index construction typically scales superlinearly (e.g., O(n log n) or worse), while query latency often grows sublinearly (e.g., logarithmic) for approximate nearest neighbor (ANN) methods. However, practical factors like memory constraints, hardware limitations, and algorithm-specific trade-offs influence real-world outcomes.

Index build time tends to grow faster than linearly as the dataset expands. For example, hierarchical navigable small world (HNSW) graphs have a construction complexity of O(n log n), meaning building an index for 1 billion vectors would take roughly 1,000 times longer than for 1 million vectors if the log factor is ignored, but closer to 1,500–2,000× when accounting for the logarithmic term. Algorithms like IVF (Inverted File Index) with k-means clustering may scale closer to O(n) but require tuning parameters like the number of clusters, which can introduce overhead. Distributed systems or GPU acceleration can mitigate this, but the underlying algorithmic complexity still dominates. For instance, a single-machine HNSW index might take hours for 1 million vectors but weeks for 1 billion without parallelization, highlighting the impracticality of naive scaling.

Query performance generally degrades sublinearly for ANN methods. HNSW query latency grows logarithmically with dataset size, so querying 1 billion vectors might only be 2–3× slower than 1 million if graph parameters (e.g., traversal depth) are held constant. However, maintaining high recall often requires adjusting these parameters, which can increase latency. IVF-based methods exhibit similar trends but depend heavily on the number of clusters searched per query—a fixed probe count may lead to linear scaling in the worst case if data distribution changes. In practice, most systems balance this by slightly increasing probes as the dataset grows, leading to sublinear but non-negligible latency increases. For example, a query taking 1ms on 1 million vectors might take 5–10ms on 1 billion with HNSW, assuming sufficient memory and optimized graph layers.

The key takeaway is that while algorithmic complexity sets the theoretical baseline, real-world scaling depends on implementation optimizations and hardware. Memory bandwidth, cache efficiency, and parallelization become critical at the billion-vector scale. Techniques like partitioning (e.g., disk-based indexes) or hybrid approaches (e.g., combining IVF with HNSW) are often necessary to manage trade-offs. Developers should prioritize algorithms with predictable scaling and test incremental growth to identify bottlenecks early.