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//! HNSW graph construction algorithm.
use crate::hnsw::distance;
use crate::hnsw::graph::{HNSWIndex, Layer};
use crate::RetrieveError;
use smallvec::SmallVec;
/// Select neighbors using RND (Relative Neighborhood Diversification).
///
/// Exact formula from 2025-2026 research: dist(X_q, X_j) < dist(X_i, X_j) for all neighbors X_i.
/// This is the best-performing ND strategy with highest pruning ratios (20-25%).
fn select_neighbors_rnd(
_query_vector: &[f32],
candidates: &[(u32, f32)],
m: usize,
vectors: &[f32],
dimension: usize,
) -> Vec<u32> {
if candidates.is_empty() {
return Vec::new();
}
// Sort by distance to query
let mut sorted: Vec<(u32, f32)> = candidates.to_vec();
sorted.sort_by(|a, b| a.1.total_cmp(&b.1));
let mut selected = Vec::with_capacity(m.min(sorted.len()));
// Start with closest candidate
if let Some((id, _)) = sorted.first() {
selected.push(*id);
}
// RND: Add candidate X_j if dist(X_q, X_j) < dist(X_i, X_j) for all selected neighbors X_i
for (candidate_id, query_to_candidate_dist) in sorted.iter().skip(1) {
if selected.len() >= m {
break;
}
let candidate_vec = get_vector(vectors, dimension, *candidate_id as usize);
let mut can_add = true;
// Check RND condition: dist(X_q, X_j) < dist(X_i, X_j) for all X_i in selected
for &selected_id in &selected {
let selected_vec = get_vector(vectors, dimension, selected_id as usize);
let inter_distance = distance::cosine_distance(selected_vec, candidate_vec);
// RND formula: query_to_candidate_dist must be < inter_distance
if *query_to_candidate_dist >= inter_distance {
can_add = false;
break;
}
}
if can_add {
selected.push(*candidate_id);
}
}
// If we still need more neighbors, add closest remaining
while selected.len() < m && selected.len() < sorted.len() {
for (id, _) in &sorted {
if !selected.contains(id) {
selected.push(*id);
break;
}
}
}
selected
}
/// Select neighbors using MOND (Maximum-Oriented Neighborhood Diversification).
///
/// Maximizes angles between neighbors. Formula: ∠(X_j X_q X_i) > θ for all selected X_i.
/// Second-best ND strategy with moderate pruning (2-4%).
fn select_neighbors_mond(
query_vector: &[f32],
candidates: &[(u32, f32)],
m: usize,
vectors: &[f32],
dimension: usize,
min_angle_degrees: f32,
) -> Vec<u32> {
if candidates.is_empty() {
return Vec::new();
}
let min_angle_rad = min_angle_degrees.to_radians();
let min_cos = min_angle_rad.cos();
// Sort by distance to query
let mut sorted: Vec<(u32, f32)> = candidates.to_vec();
sorted.sort_by(|a, b| a.1.total_cmp(&b.1));
let mut selected = Vec::with_capacity(m.min(sorted.len()));
// Start with closest candidate
if let Some((id, _)) = sorted.first() {
selected.push(*id);
}
// MOND: Add candidate if angle with all selected neighbors > min_angle
for (candidate_id, _) in sorted.iter().skip(1) {
if selected.len() >= m {
break;
}
let candidate_vec = get_vector(vectors, dimension, *candidate_id as usize);
let mut can_add = true;
// Compute angle between query->candidate and query->selected for each selected neighbor
// Optimized: avoid temporary Vec allocations, use SIMD-accelerated operations
use crate::simd;
for &selected_id in &selected {
let selected_vec = get_vector(vectors, dimension, selected_id as usize);
// Compute difference vectors inline (avoid allocations)
// q_to_c = candidate_vec - query_vector
// q_to_s = selected_vec - query_vector
// We compute dot(q_to_c, q_to_s) and norms without creating temporary Vecs
// Use identity: dot(a-b, c-b) = dot(a,c) - dot(a,b) - dot(c,b) + dot(b,b)
// For our case: dot(q_to_c, q_to_s) = dot(candidate_vec, selected_vec)
// - dot(candidate_vec, query) - dot(selected_vec, query) + dot(query, query)
let dot_cc = simd::dot(candidate_vec, selected_vec);
let dot_cq = simd::dot(candidate_vec, query_vector);
let dot_sq = simd::dot(selected_vec, query_vector);
let dot_qq = simd::dot(query_vector, query_vector);
let dot_qc_qs = dot_cc - dot_cq - dot_sq + dot_qq;
// Compute norms: norm(a-b)^2 = norm(a)^2 + norm(b)^2 - 2*dot(a,b)
let norm_c_sq = simd::dot(candidate_vec, candidate_vec) + dot_qq - 2.0 * dot_cq;
let norm_s_sq = simd::dot(selected_vec, selected_vec) + dot_qq - 2.0 * dot_sq;
if norm_c_sq > 0.0 && norm_s_sq > 0.0 {
let norm_c = norm_c_sq.sqrt();
let norm_s = norm_s_sq.sqrt();
let cos_angle = dot_qc_qs / (norm_c * norm_s);
// Angle > min_angle means cos(angle) < cos(min_angle) (since cosine is decreasing)
if cos_angle >= min_cos {
can_add = false;
break;
}
}
}
if can_add {
selected.push(*candidate_id);
}
}
// If we still need more neighbors, add closest remaining
while selected.len() < m && selected.len() < sorted.len() {
for (id, _) in &sorted {
if !selected.contains(id) {
selected.push(*id);
break;
}
}
}
selected
}
/// Select neighbors using RRND (Relaxed Relative Neighborhood Diversification).
///
/// Formula: dist(X_q, X_j) < α · dist(X_i, X_j) with α ≥ 1.5.
/// Less effective than RND, creates larger graphs.
fn select_neighbors_rrnd(
_query_vector: &[f32],
candidates: &[(u32, f32)],
m: usize,
vectors: &[f32],
dimension: usize,
alpha: f32,
) -> Vec<u32> {
if candidates.is_empty() {
return Vec::new();
}
// Sort by distance to query
let mut sorted: Vec<(u32, f32)> = candidates.to_vec();
sorted.sort_by(|a, b| a.1.total_cmp(&b.1));
let mut selected = Vec::with_capacity(m.min(sorted.len()));
// Start with closest candidate
if let Some((id, _)) = sorted.first() {
selected.push(*id);
}
// RRND: Add candidate X_j if dist(X_q, X_j) < α · dist(X_i, X_j) for all selected X_i
for (candidate_id, query_to_candidate_dist) in sorted.iter().skip(1) {
if selected.len() >= m {
break;
}
let candidate_vec = get_vector(vectors, dimension, *candidate_id as usize);
let mut can_add = true;
for &selected_id in &selected {
let selected_vec = get_vector(vectors, dimension, selected_id as usize);
let inter_distance = distance::cosine_distance(selected_vec, candidate_vec);
// RRND formula: query_to_candidate_dist < alpha * inter_distance
if *query_to_candidate_dist >= alpha * inter_distance {
can_add = false;
break;
}
}
if can_add {
selected.push(*candidate_id);
}
}
// If we still need more neighbors, add closest remaining
while selected.len() < m && selected.len() < sorted.len() {
for (id, _) in &sorted {
if !selected.contains(id) {
selected.push(*id);
break;
}
}
}
selected
}
/// Select neighbors based on configured diversification strategy.
pub fn select_neighbors(
query_vector: &[f32],
candidates: &[(u32, f32)],
m: usize,
vectors: &[f32],
dimension: usize,
strategy: &crate::hnsw::graph::NeighborhoodDiversification,
) -> Vec<u32> {
match strategy {
crate::hnsw::graph::NeighborhoodDiversification::RelativeNeighborhood => {
select_neighbors_rnd(query_vector, candidates, m, vectors, dimension)
}
crate::hnsw::graph::NeighborhoodDiversification::MaximumOriented { min_angle_degrees } => {
select_neighbors_mond(
query_vector,
candidates,
m,
vectors,
dimension,
*min_angle_degrees,
)
}
crate::hnsw::graph::NeighborhoodDiversification::RelaxedRelative { alpha } => {
select_neighbors_rrnd(query_vector, candidates, m, vectors, dimension, *alpha)
}
}
}
/// Get vector from SoA storage.
pub fn get_vector(vectors: &[f32], dimension: usize, idx: usize) -> &[f32] {
let start = idx * dimension;
let end = start + dimension;
&vectors[start..end]
}
/// Construct HNSW graph layers.
///
/// Implements the insertion algorithm from the HNSW paper (Malkov & Yashunin, 2018).
///
/// Key insight: When descending through layers, we use the closest node found
/// in the layer above as the entry point for the next layer. This ensures
/// we start searching from a good position, not an arbitrary node.
pub fn construct_graph(index: &mut HNSWIndex) -> Result<(), RetrieveError> {
if index.num_vectors == 0 {
return Err(RetrieveError::EmptyIndex);
}
// Find maximum layer
let max_layer = index.layer_assignments.iter().max().copied().unwrap_or(0) as usize;
// Initialize layers with uncompressed storage
index.layers = (0..=max_layer)
.map(|_| Layer::new_uncompressed(vec![SmallVec::new(); index.num_vectors]))
.collect();
// Global entry point: node in highest layer (updated as we insert)
let mut global_entry_point = 0u32;
let mut global_entry_layer = 0u8;
for (idx, &layer) in index.layer_assignments.iter().enumerate() {
if layer > global_entry_layer {
global_entry_point = idx as u32;
global_entry_layer = layer;
}
}
// Insert each vector into the graph
for current_id in 0..index.num_vectors {
let current_layer = index.layer_assignments[current_id] as usize;
let current_vector = index.get_vector(current_id).to_vec(); // Copy to avoid borrowing
// Track closest node found while descending through upper layers.
// This is the key fix: we propagate the closest node down through layers
// instead of always starting from node 0.
let mut layer_entry_point = global_entry_point;
// For each layer from current_layer down to 0
for layer_idx in (0..=current_layer.min(max_layer)).rev() {
// Find candidates in this layer, starting from best entry point
let mut candidates = Vec::with_capacity(index.params.ef_construction);
let to_explore = vec![layer_entry_point];
let mut visited =
std::collections::HashSet::with_capacity(index.params.ef_construction);
// Explore up to ef_construction candidates
// Use VecDeque for O(1) pop_front instead of O(n) remove(0)
use std::collections::VecDeque;
let mut to_explore_deque: VecDeque<u32> = to_explore.into_iter().collect();
while let Some(explore_id) = to_explore_deque.pop_front() {
if candidates.len() >= index.params.ef_construction {
break;
}
if visited.contains(&explore_id) {
continue;
}
visited.insert(explore_id);
let explore_vec = index.get_vector(explore_id as usize);
let dist = distance::cosine_distance(¤t_vector, explore_vec);
candidates.push((explore_id, dist));
// Add neighbors to explore (borrow layer immutably)
if layer_idx < index.layers.len() {
let neighbors = index.layers[layer_idx].get_neighbors(explore_id);
for &neighbor_id in neighbors.iter() {
if !visited.contains(&neighbor_id) {
to_explore_deque.push_back(neighbor_id);
}
}
}
}
// Update entry point for next layer: use closest candidate found
// This is crucial for HNSW performance - we want to start the next
// layer's search from the best position found so far.
if !candidates.is_empty() {
let closest = candidates
.iter()
.min_by(|a, b| a.1.total_cmp(&b.1))
.map(|(id, _)| *id)
.unwrap_or(layer_entry_point);
layer_entry_point = closest;
}
// Select neighbors using configured diversification strategy
let m_actual = if layer_idx == 0 {
index.params.m_max
} else {
index.params.m
};
let selected = select_neighbors(
¤t_vector,
&candidates,
m_actual,
&index.vectors,
index.dimension,
&index.params.neighborhood_diversification,
);
// Pre-compute all neighbor vectors and distances (before any mutable borrows)
// selected contains the new neighbors we want to add
let neighbor_data: Vec<(u32, Vec<f32>, f32)> = selected
.iter()
.map(|&id| {
let vec = index.get_vector(id as usize);
let dist = distance::cosine_distance(¤t_vector, vec);
(id, vec.to_vec(), dist) // Copy vector to avoid borrowing
})
.collect();
// Pre-compute existing neighbors of current_id
let current_existing_neighbors: Vec<u32> = if layer_idx < index.layers.len() {
index.layers[layer_idx]
.get_neighbors(current_id as u32)
.iter()
.copied()
.collect()
} else {
Vec::new()
};
// Pre-compute distances from current to ALL its neighbors (existing + selected)
// Use HashMap for O(1) lookup during pruning
let mut all_current_distances: std::collections::HashMap<u32, f32> =
std::collections::HashMap::with_capacity(
current_existing_neighbors.len() + selected.len(),
);
// Add distances to existing neighbors
for &id in ¤t_existing_neighbors {
let vec = index.get_vector(id as usize);
let dist = distance::cosine_distance(¤t_vector, vec);
all_current_distances.insert(id, dist);
}
// Add distances to selected neighbors
for (nid, _, dist) in &neighbor_data {
all_current_distances.insert(*nid, *dist);
}
// Pre-compute existing neighbor data for reverse connections
let existing_neighbor_lists: Vec<Vec<u32>> = selected
.iter()
.map(|&neighbor_id| {
if layer_idx < index.layers.len() {
index.layers[layer_idx]
.get_neighbors(neighbor_id)
.iter()
.copied()
.collect()
} else {
Vec::new()
}
})
.collect();
// Pre-compute distances for each selected neighbor to ALL its potential neighbors
// This includes: existing neighbors of that node + current_id
let mut all_reverse_distances: Vec<std::collections::HashMap<u32, f32>> = Vec::new();
for (idx, _) in selected.iter().enumerate() {
let neighbor_vec = &neighbor_data[idx].1;
let mut distances = std::collections::HashMap::new();
// Distance to current_id
distances.insert(current_id as u32, neighbor_data[idx].2);
// Distances to existing neighbors
for &existing_id in &existing_neighbor_lists[idx] {
let existing_vec = index.get_vector(existing_id as usize);
let dist = distance::cosine_distance(neighbor_vec, existing_vec);
distances.insert(existing_id, dist);
}
all_reverse_distances.push(distances);
}
// Now do all mutable operations
let layer = &mut index.layers[layer_idx];
let neighbors_vec = layer.get_neighbors_mut();
// First pass: add all edges without pruning
for &neighbor_id in &selected {
let neighbors = &mut neighbors_vec[current_id];
if !neighbors.contains(&neighbor_id) {
neighbors.push(neighbor_id);
}
let reverse_neighbors = &mut neighbors_vec[neighbor_id as usize];
if !reverse_neighbors.contains(&(current_id as u32)) {
reverse_neighbors.push(current_id as u32);
}
}
// Second pass: prune current_id's neighbors if needed
{
let neighbors = &mut neighbors_vec[current_id];
if neighbors.len() > m_actual {
let mut neighbor_candidates: Vec<(u32, f32)> = neighbors
.iter()
.map(|&id| {
let dist =
all_current_distances.get(&id).copied().unwrap_or_else(|| {
// Compute distance on the fly if somehow missing
let vec =
get_vector(&index.vectors, index.dimension, id as usize);
distance::cosine_distance(¤t_vector, vec)
});
(id, dist)
})
.collect();
neighbor_candidates.sort_by(|a, b| a.1.total_cmp(&b.1));
neighbor_candidates.truncate(m_actual);
*neighbors = neighbor_candidates.iter().map(|(id, _)| *id).collect();
}
}
// Third pass: prune each selected neighbor's reverse list if needed
for (idx, &neighbor_id) in selected.iter().enumerate() {
let reverse_neighbors = &mut neighbors_vec[neighbor_id as usize];
if reverse_neighbors.len() > m_actual {
let distances = &all_reverse_distances[idx];
let neighbor_vec = &neighbor_data[idx].1;
let mut reverse_candidates: Vec<(u32, f32)> = reverse_neighbors
.iter()
.map(|&id| {
let dist = distances.get(&id).copied().unwrap_or_else(|| {
// Compute distance on the fly if somehow missing
let vec = get_vector(&index.vectors, index.dimension, id as usize);
distance::cosine_distance(neighbor_vec, vec)
});
(id, dist)
})
.collect();
reverse_candidates.sort_by(|a, b| a.1.total_cmp(&b.1));
reverse_candidates.truncate(m_actual);
*reverse_neighbors = reverse_candidates.iter().map(|(id, _)| *id).collect();
}
}
}
}
Ok(())
}