Add parallel BKT tree build support via level-order BFS with OpenMP

[xufyan]

Summary

Add a parallel BKT (Balanced K-means Tree) build option that dramatically accelerates tree construction for large datasets. The existing BuildTrees() method uses a depth-first recursive approach where each tree level is built sequentially. The new BuildTreesParallel() method uses a level-order (BFS) approach with OpenMP to process all sibling nodes at each level in parallel.

Motivation

For large-scale SPANN indexes (e.g., 50M+ vectors), the Select Head phase — where BKT construction contributes a large portion of the build time — becomes a major bottleneck. On a 50M SIFT dataset, the sequential BKT build takes ~16.6 hours with 16 threads because only 1 thread is active at deeper tree levels. The parallel approach reduces this to ~1.2 hours with 32 threads, a 13.6x speedup.

Design

The parallel build works by:

1. Level-order traversal: Instead of recursive DFS, the tree is built level-by-level (BFS)
2. Parallel k-means: At each level, all sibling nodes run independent k-means clustering in parallel via #pragma omp parallel for
3. Sequential assembly: After each parallel phase, the tree structure is assembled sequentially to maintain correctness
4. Thread-local resources: Each parallel k-means task uses its own KmeansArgs with 1 thread (parallelism is at the node level, not within k-means)

This is an opt-in feature controlled by a new ParallelBKTBuild parameter (default: false), so there is zero impact on existing behavior.

Changes

File	Change
BKTree.h	Add BuildTreesParallel() method + m_parallelBuild member
BKT/ParameterDefinitionList.h	Add ParallelBKTBuild parameter for BKT index
SPANN/Options.h	Add m_parallelBKTBuild option
SPANN/ParameterDefinitionList.h	Add ParallelBKTBuild parameter for SPANN select head
BKTIndex.cpp	Dispatch to parallel or sequential build based on flag
SPANNIndex.cpp	Pass ParallelBKTBuild flag and dispatch accordingly

Benchmark Results

Dataset: SIFT 50M vectors, 128-dim float, L2 distance
Hardware: Azure Standard_L32s_v2 (32 vCPUs, AMD EPYC 7551, 256 GiB RAM)

BKT Build Time Comparison

Phase	Sequential (16 threads)	Parallel (32 threads)	Speedup
Select Head BKT build	16.6 hours	1.2 hours	13.6x
Build Head BKT build	2.12 hours	8.65 minutes	14.7x

Usage

Enable in config:

[SelectHead]
ParallelBKTBuild=true
NumberOfThreads=32

Or for BKT index directly:

[Index]
ParallelBKTBuild=true

[xufyan]

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