This isn’t as simple as measuring loudness. Human speech includes pauses, hesitations, filler sounds, background noise, and non-verbal acknowledgements that shouldn’t interrupt the agent. Downstream from this are the things everyone notices: end-to-end latency, awkward silences, agents cutting you off, or talking over you.
The algorithm maintains a running "best distance" that starts at infinity. As it walks the tree, it checks each visited point and updates the best distance if it finds something closer. Before recursing into a child node, it checks whether the closest possible point in that child's bounding box is farther than the current best. If so, the entire subtree gets pruned.
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