# Constrained k-nearest-neighbor search

Constrained vector search with per-category caps previously relied on a fixed visit budget or on stopping rules trained for average recall, neither of which guarantees an exact answer. CaST restricts stopping rules to a monotone class over a declared interface, calibrates them with fixed-sequence binomial tests, and derives a lower bound on the class-optimal cost via Lagrangian weak duality. On two datasets of one million items each, its replayed cost is at most 1.132 times the class optimum for risk levels 0.03 to 0.10 at 95% confidence, and at a 0.05 risk target its mean latency is lower than every other calibrated rule timed.

Constrained vector search with per-category caps previously relied on a fixed visit budget or on stopping rules trained for average recall, neither of which guarantees an exact answer. CaST restricts stopping rules to a monotone class over a declared interface, calibrates them with fixed-sequence binomial tests, and derives a lower bound on the class-optimal cost via Lagrangian weak duality. On two datasets of one million items each, its replayed cost is at most 1.132 times the class optimum for risk levels 0.03 to 0.10 at 95% confidence, and at a 0.05 risk target its mean latency is lower than every other calibrated rule timed.