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+# RFC: Vector Index with USearch (HNSW)
+
+- Feature Name: `vector-index-usearch`
+- Start Date: 2024-12-04
+- RFC PR: (leave this empty)
+- Issue: (leave this empty)
+
+## Summary
+
+Integrate USearch library to enable Approximate Nearest Neighbor (ANN) search for vector columns in GreptimeDB, replacing the current O(N) brute-force approach with O(log N) HNSW-based indexing.
+
+## Motivation
+
+The current vector search implementation uses [nalgebra](https://docs.rs/nalgebra/latest/nalgebra/) for brute-force distance calculation. While simple and accurate, this approach has O(N) complexity, making it impractical for tables with millions of rows.
+
+Vector similarity search is fundamental to:
+- Retrieval-Augmented Generation (RAG) pipelines
+- Semantic search applications
+- Recommendation systems
+- Anomaly detection via embedding comparison
+
+To support these use cases at scale, GreptimeDB needs an efficient vector index structure.
+
+### Goals
+
+1. **Performance**: Achieve sub-linear search complexity through HNSW indexing
+2. **Transparency**: Automatically optimize eligible queries without SQL changes
+3. **Compatibility**: Preserve existing vector functions as fallback
+4. **Persistence**: Store indexes in SST files via Puffin blob format
+5. **Configurability**: Expose HNSW parameters for tuning recall vs. performance
+
+### Non-Goals
+
+1. Exact nearest neighbor search (covered by existing brute-force)
+2. GPU-accelerated vector operations
+3. Distributed vector index across datanodes
+4. Real-time index updates (follows SST lifecycle)
+
+## Design Overview
+
+### Architecture
+
+```
+┌─────────────────────────────────────────────────────────────┐
+│                      Query Layer                            │
+│  ┌─────────────────────────────────────────────────────┐   │
+│  │           VectorSearchOptimizer (new)               │   │
+│  │  Detects: ORDER BY vec_*_distance() LIMIT k         │   │
+│  └─────────────────────────────────────────────────────┘   │
+└─────────────────────────────────────────────────────────────┘
+                              │
+                              ▼
+┌─────────────────────────────────────────────────────────────┐
+│                     Storage Layer                           │
+│  ┌──────────────────────┐    ┌──────────────────────────┐  │
+│  │   VectorIndexer      │    │  VectorIndexApplier      │  │
+│  │   (write path)       │    │  (read path)             │  │
+│  └──────────────────────┘    └──────────────────────────┘  │
+│                              │                              │
+│                              ▼                              │
+│  ┌─────────────────────────────────────────────────────┐   │
+│  │              USearch Index (HNSW)                    │   │
+│  │              Stored in Puffin Blob                   │   │
+│  └─────────────────────────────────────────────────────┘   │
+└─────────────────────────────────────────────────────────────┘
+```
+
+### USearch Library
+
+| Property | Value |
+|----------|-------|
+| Crate | `usearch = "2.21.4"` |
+| Algorithm | HNSW (Hierarchical Navigable Small World) |
+| Binding | C++ via cxx |
+| Metrics | Cosine, L2 squared, Inner Product, Hamming |
+| Quantization | f32, f64, f16, i8 |
+
+## Detailed Design
+
+### 1. Index Configuration
+
+```rust
+/// Vector index configuration stored in column metadata
+#[derive(Debug, Clone, Serialize, Deserialize)]
+pub struct VectorIndexConfig {
+    /// HNSW connectivity parameter (M)
+    /// Higher values improve recall but increase memory and build time
+    /// Typical range: 8-64, default: 16
+    pub connectivity: usize,
+
+    /// HNSW expansion factor for index construction (efConstruction)
+    /// Higher values improve index quality but increase build time
+    /// Typical range: 64-512, default: 128
+    pub expansion_add: usize,
+
+    /// HNSW expansion factor for search (ef)
+    /// Higher values improve recall but increase search latency
+    /// Typical range: 32-256, default: 64
+    pub expansion_search: usize,
+
+    /// Distance metric (must match query function)
+    pub metric: VectorMetric,
+
+    /// Optional memory limit for index cache
+    pub memory_limit_bytes: Option<usize>,
+}
+
+#[derive(Debug, Clone, Copy, Serialize, Deserialize)]
+pub enum VectorMetric {
+    Cosine,
+    L2Squared,
+    InnerProduct,
+}
+
+impl Default for VectorIndexConfig {
+    fn default() -> Self {
+        Self {
+            connectivity: 16,
+            expansion_add: 128,
+            expansion_search: 64,
+            metric: VectorMetric::Cosine,
+            memory_limit_bytes: None,
+        }
+    }
+}
+```
+
+### 2. DDL Syntax
+
+```sql
+-- Create table with vector index
+CREATE TABLE embeddings (
+    ts TIMESTAMP TIME INDEX,
+    id STRING PRIMARY KEY,
+    vec VECTOR(384) VECTOR INDEX WITH (
+        type = 'hnsw',
+        metric = 'cosine',
+        connectivity = 16,
+        expansion_add = 128,
+        expansion_search = 64
+    )
+);
+
+-- Add index to existing column
+ALTER TABLE embeddings
+ADD VECTOR INDEX idx_vec ON vec WITH (
+    type = 'hnsw',
+    metric = 'l2sq'
+);
+
+-- Drop vector index
+ALTER TABLE embeddings DROP VECTOR INDEX idx_vec;
+```
+
+### 3. Index Building (Write Path)
+
+The `VectorIndexer` integrates with the existing indexer lifecycle in mito2:
+
+```rust
+pub struct VectorIndexer {
+    /// Column metadata
+    column_id: ColumnId,
+    dimensions: u32,
+
+    /// HNSW configuration
+    config: VectorIndexConfig,
+
+    /// In-memory index being built
+    index: Index,
+
+    /// Row key counter (used as HNSW key)
+    row_count: u64,
+
+    /// Memory tracking
+    memory_usage: Arc<AtomicUsize>,
+}
+
+impl Indexer for VectorIndexer {
+    /// Called for each row during SST write
+    fn update(&mut self, row_id: u64, value: &Value) -> Result<()> {
+        let vector = match value {
+            Value::Binary(bytes) => bytes_to_f32_vec(bytes)?,
+            Value::Null => return Ok(()), // Skip null values
+            _ => return Err(Error::InvalidVectorData),
+        };
+
+        // Validate dimension
+        if vector.len() != self.dimensions as usize {
+            return Err(Error::DimensionMismatch {
+                expected: self.dimensions,
+                actual: vector.len(),
+            });
+        }
+
+        // Add to HNSW index with row_id as key
+        self.index.add(row_id, &vector)?;
+        self.row_count += 1;
+        self.update_memory_usage();
+
+        Ok(())
+    }
+
+    /// Serialize index to Puffin blob
+    fn finish(&mut self) -> Result<Vec<u8>> {
+        if self.row_count == 0 {
+            return Ok(Vec::new());
+        }
+
+        let mut buffer = Vec::new();
+
+        // Header: version + config
+        buffer.extend_from_slice(&VECTOR_INDEX_VERSION.to_le_bytes());
+        let config_bytes = bincode::serialize(&self.config)?;
+        buffer.extend_from_slice(&(config_bytes.len() as u32).to_le_bytes());
+        buffer.extend_from_slice(&config_bytes);
+
+        // Index data
+        self.index.save_to_buffer(&mut buffer)?;
+
+        Ok(buffer)
+    }
+
+    fn abort(&mut self) {
+        // Index dropped automatically
+    }
+
+    fn memory_usage(&self) -> usize {
+        self.memory_usage.load(Ordering::Relaxed)
+    }
+}
+```
+
+#### Puffin Blob Format
+
+```
+┌─────────────────────────────────────────┐
+│  Vector Index Blob                      │
+├─────────────────────────────────────────┤
+│  version: u32 (1)                       │
+│  config_len: u32                        │
+│  config: VectorIndexConfig (bincode)    │
+│  index_data: [u8] (USearch binary)      │
+└─────────────────────────────────────────┘
+```
+
+### 4. Query Execution (Read Path)
+
+#### 4.1 Query Pattern Detection
+
+The `VectorSearchOptimizer` identifies queries eligible for ANN optimization:
+
+```rust
+impl PhysicalOptimizerRule for VectorSearchOptimizer {
+    fn optimize(
+        &self,
+        plan: Arc<dyn ExecutionPlan>,
+        config: &ConfigOptions,
+    ) -> Result<Arc<dyn ExecutionPlan>> {
+        // Pattern: TopK(Sort(Scan))
+        // Where Sort is ORDER BY vec_*_distance(column, constant)
+
+        let Some(topk) = plan.as_any().downcast_ref::<TopKExec>() else {
+            return Ok(plan);
+        };
+
+        let sort_exprs = topk.sort_exprs();
+        if sort_exprs.len() != 1 {
+            return Ok(plan);
+        }
+
+        let (column, query_vector, metric) =
+            match extract_vector_distance_expr(&sort_exprs[0].expr) {
+                Some(info) => info,
+                None => return Ok(plan),
+            };
+
+        // Check if column has vector index
+        let index_meta = self.get_vector_index_meta(&column)?;
+        if index_meta.is_none() {
+            return Ok(plan); // Fall back to brute-force
+        }
+
+        // Verify metric compatibility
+        let index_meta = index_meta.unwrap();
+        if !is_metric_compatible(&metric, &index_meta.config.metric) {
+            return Ok(plan);
+        }
+
+        // Replace with VectorAnnScan
+        Ok(Arc::new(VectorAnnScanExec::new(
+            column,
+            query_vector,
+            topk.fetch().unwrap_or(10),
+            index_meta,
+            topk.input().clone(),
+        )))
+    }
+}
+
+fn extract_vector_distance_expr(
+    expr: &Arc<dyn PhysicalExpr>
+) -> Option<(Column, Vec<f32>, VectorMetric)> {
+    let func = expr.as_any().downcast_ref::<ScalarFunctionExpr>()?;
+
+    let metric = match func.name() {
+        "vec_cos_distance" => VectorMetric::Cosine,
+        "vec_l2sq_distance" => VectorMetric::L2Squared,
+        "vec_dot_product" => VectorMetric::InnerProduct,
+        _ => return None,
+    };
+
+    // Extract column and constant vector from arguments
+    let args = func.args();
+    if args.len() != 2 {
+        return None;
+    }
+
+    // Try both argument orders: (column, const) or (const, column)
+    try_extract_column_and_vector(&args[0], &args[1], metric)
+        .or_else(|| try_extract_column_and_vector(&args[1], &args[0], metric))
+}
+```
+
+#### 4.2 Index Loading and Search
+
+```rust
+pub struct VectorIndexApplier {
+    /// Index configuration
+    config: VectorIndexConfig,
+
+    /// Loaded index (lazily initialized)
+    index: Option<Index>,
+
+    /// Index data reference
+    blob_reader: Arc<dyn BlobReader>,
+
+    /// Cache for loaded indexes
+    cache: Arc<VectorIndexCache>,
+}
+
+impl VectorIndexApplier {
+    /// Load index from Puffin blob
+    pub fn load(&mut self) -> Result<()> {
+        if self.index.is_some() {
+            return Ok(());
+        }
+
+        // Check cache first
+        let cache_key = self.blob_reader.blob_id();
+        if let Some(cached) = self.cache.get(&cache_key) {
+            self.index = Some(cached);
+            return Ok(());
+        }
+
+        // Read blob data
+        let data = self.blob_reader.read_all()?;
+        if data.is_empty() {
+            return Ok(()); // No index (empty SST)
+        }
+
+        // Parse header
+        let version = u32::from_le_bytes(data[0..4].try_into()?);
+        if version != VECTOR_INDEX_VERSION {
+            return Err(Error::UnsupportedIndexVersion(version));
+        }
+
+        let config_len = u32::from_le_bytes(data[4..8].try_into()?) as usize;
+        let config: VectorIndexConfig = bincode::deserialize(&data[8..8+config_len])?;
+
+        // Load USearch index
+        let index_data = &data[8+config_len..];
+        let options = IndexOptions {
+            dimensions: self.dimensions as usize,
+            metric: config.metric.into(),
+            quantization: ScalarKind::F32,
+            connectivity: config.connectivity,
+            expansion_add: config.expansion_add,
+            expansion_search: config.expansion_search,
+            multi: false,
+        };
+
+        let index = Index::new(&options)?;
+        index.load_from_buffer(index_data)?;
+
+        // Cache the loaded index
+        self.cache.insert(cache_key, index.clone());
+        self.index = Some(index);
+
+        Ok(())
+    }
+
+    /// Perform ANN search, returns row IDs sorted by distance
+    pub fn search(&self, query: &[f32], k: usize) -> Result<Vec<(u64, f32)>> {
+        let index = self.index.as_ref()
+            .ok_or(Error::IndexNotLoaded)?;
+
+        let matches = index.search(query, k)?;
+
+        Ok(matches.keys.into_iter()
+            .zip(matches.distances.into_iter())
+            .collect())
+    }
+}
+```
+
+#### 4.3 Multi-SST Query Execution
+
+When a query spans multiple SST files, each SST's index is searched independently and results are merged:
+
+```rust
+pub struct VectorAnnScanExec {
+    column: Column,
+    query_vector: Vec<f32>,
+    k: usize,
+    sst_readers: Vec<SstReader>,
+}
+
+impl ExecutionPlan for VectorAnnScanExec {
+    fn execute(&self, partition: usize, context: Arc<TaskContext>)
+        -> Result<SendableRecordBatchStream>
+    {
+        let mut all_candidates: Vec<(u64, f32, SstId)> = Vec::new();
+
+        // Search each SST's index
+        for reader in &self.sst_readers {
+            let applier = reader.vector_index_applier(&self.column)?;
+
+            if let Some(mut applier) = applier {
+                applier.load()?;
+
+                // Request more candidates from each SST for better recall
+                let candidates = applier.search(
+                    &self.query_vector,
+                    self.k * 2  // Over-fetch for merge accuracy
+                )?;
+
+                for (row_id, distance) in candidates {
+                    all_candidates.push((row_id, distance, reader.sst_id()));
+                }
+            } else {
+                // No index: fall back to brute-force for this SST
+                let candidates = self.brute_force_search(reader)?;
+                all_candidates.extend(candidates);
+            }
+        }
+
+        // Sort by distance and take top-k
+        all_candidates.sort_by(|a, b| a.1.partial_cmp(&b.1).unwrap());
+        all_candidates.truncate(self.k);
+
+        // Fetch actual rows by row_id
+        self.fetch_rows(all_candidates, context)
+    }
+}
+```
+
+### 5. Compaction Handling
+
+HNSW graphs cannot be merged incrementally. During compaction, vector indexes must be fully rebuilt:
+
+```rust
+impl CompactionTask {
+    fn merge_sst_files(&self, inputs: Vec<SstReader>) -> Result<SstWriter> {
+        let mut writer = SstWriter::new(self.output_path)?;
+
+        // Check if any input has vector index
+        let has_vector_index = inputs.iter()
+            .any(|r| r.has_vector_index(&self.vector_column));
+
+        if has_vector_index {
+            // Create new indexer for output SST
+            let indexer = VectorIndexer::new(
+                self.vector_column.clone(),
+                self.vector_config.clone(),
+            );
+            writer.set_vector_indexer(indexer);
+        }
+
+        // Iterate all rows from input SSTs
+        let mut row_id = 0u64;
+        for input in inputs {
+            for row in input.iter()? {
+                // Write row to new SST
+                writer.write_row(&row)?;
+
+                // Update vector index with new row_id mapping
+                if has_vector_index {
+                    if let Some(vector_value) = row.get(&self.vector_column) {
+                        writer.vector_indexer_mut()
+                            .update(row_id, vector_value)?;
+                    }
+                }
+                row_id += 1;
+            }
+        }
+
+        writer.finish()
+    }
+}
+```
+
+### 6. Memory Management
+
+#### 6.1 Index Cache
+
+```rust
+pub struct VectorIndexCache {
+    /// LRU cache: blob_id -> loaded Index
+    cache: Mutex<LruCache<BlobId, Arc<Index>>>,
+
+    /// Current memory usage
+    memory_usage: AtomicUsize,
+
+    /// Maximum memory limit
+    memory_limit: usize,
+}
+
+impl VectorIndexCache {
+    pub fn new(memory_limit: usize) -> Self {
+        // Estimate max entries based on typical index size
+        let estimated_max_entries = memory_limit / (10 * 1024 * 1024); // ~10MB per index
+
+        Self {
+            cache: Mutex::new(LruCache::new(
+                NonZeroUsize::new(estimated_max_entries.max(16)).unwrap()
+            )),
+            memory_usage: AtomicUsize::new(0),
+            memory_limit,
+        }
+    }
+
+    pub fn get(&self, key: &BlobId) -> Option<Arc<Index>> {
+        self.cache.lock().get(key).cloned()
+    }
+
+    pub fn insert(&self, key: BlobId, index: Index) {
+        let index_size = index.memory_usage();
+        let index = Arc::new(index);
+
+        let mut cache = self.cache.lock();
+
+        // Evict if necessary
+        while self.memory_usage.load(Ordering::Relaxed) + index_size > self.memory_limit {
+            if let Some((_, evicted)) = cache.pop_lru() {
+                self.memory_usage.fetch_sub(
+                    evicted.memory_usage(),
+                    Ordering::Relaxed
+                );
+            } else {
+                break;
+            }
+        }
+
+        cache.put(key, index);
+        self.memory_usage.fetch_add(index_size, Ordering::Relaxed);
+    }
+}
+```
+
+#### 6.2 Memory-Mapped Loading (Future Enhancement)
+
+For very large indexes, memory-mapped loading can reduce memory pressure:
+
+```rust
+impl VectorIndexApplier {
+    /// Load index using memory-mapped file (future enhancement)
+    pub fn load_mmap(&mut self, path: &Path) -> Result<()> {
+        let index = Index::new(&self.options)?;
+
+        // USearch supports view_from_file for memory-mapped access
+        // This loads the index structure but keeps vectors on disk
+        unsafe {
+            index.view_from_file(path)?;
+        }
+
+        self.index = Some(index);
+        Ok(())
+    }
+}
+```
+
+### 7. Existing Vector Functions
+
+The existing vector functions remain unchanged and serve as fallback:
+
+| Function | Purpose | Index Relationship |
+|----------|---------|-------------------|
+| `parse_vec` | String → Binary | Data ingestion |
+| `vec_to_string` | Binary → String | Data display |
+| `vec_cos_distance` | Cosine distance | **Optimizer trigger** / Fallback |
+| `vec_l2sq_distance` | L2 squared distance | **Optimizer trigger** / Fallback |
+| `vec_dot_product` | Inner product | **Optimizer trigger** / Fallback |
+| `vec_add/sub/mul/div` | Arithmetic | Independent |
+| `vec_norm/dim/kth_elem` | Utilities | Independent |
+| `scalar_add/mul` | Scalar ops | Independent |
+| `elem_sum/product/avg` | Aggregation | Independent |
+
+The distance functions serve dual purposes:
+1. **Optimizer trigger**: Query patterns like `ORDER BY vec_cos_distance(col, query) LIMIT k` are detected and rewritten to use ANN scan
+2. **Brute-force fallback**: When no index exists or query is ineligible, the original nalgebra implementation executes
+
+## Implementation Plan
+
+### Phase 1: Core Infrastructure
+- [ ] Add `usearch` dependency to `src/mito2/Cargo.toml`
+- [ ] Implement `VectorIndexConfig` in `src/mito2/src/sst/index/vector/`
+- [ ] Implement `VectorIndexer` for write path
+- [ ] Add Puffin blob integration for vector index storage
+
+### Phase 2: Query Path
+- [ ] Implement `VectorIndexApplier` for read path
+- [ ] Implement `VectorIndexCache` with LRU eviction
+- [ ] Add `VectorSearchOptimizer` physical optimizer rule
+- [ ] Implement `VectorAnnScanExec` execution plan
+
+### Phase 3: Compaction & DDL
+- [ ] Update compaction to rebuild vector indexes
+- [ ] Add DDL parser support for `VECTOR INDEX`
+- [ ] Add `ALTER TABLE ADD/DROP VECTOR INDEX`
+
+### Phase 4: Testing & Documentation
+- [ ] Unit tests for indexer and applier
+- [ ] Integration tests for end-to-end queries
+- [ ] Benchmark suite comparing brute-force vs. HNSW
+- [ ] User documentation
+
+## Files to Modify
+
+| Path | Change |
+|------|--------|
+| `src/mito2/Cargo.toml` | Add `usearch = "2.21.4"` |
+| `src/mito2/src/sst/index/mod.rs` | Add `vector` module |
+| `src/mito2/src/sst/index/vector/mod.rs` | New: VectorIndexer, VectorIndexApplier |
+| `src/mito2/src/sst/index/vector/config.rs` | New: VectorIndexConfig |
+| `src/mito2/src/sst/index/vector/cache.rs` | New: VectorIndexCache |
+| `src/mito2/src/sst/parquet/writer.rs` | Integrate VectorIndexer |
+| `src/mito2/src/sst/parquet/reader.rs` | Load vector index from Puffin |
+| `src/mito2/src/compaction/` | Rebuild vector index during compaction |
+| `src/query/src/optimizer/` | Add VectorSearchOptimizer |
+| `src/query/src/physical_plan/` | Add VectorAnnScanExec |
+| `src/sql/src/parsers/` | Parse VECTOR INDEX DDL |
+| `src/common/function/src/scalars/vector/` | No changes (fallback preserved) |
+
+## Alternatives Considered
+
+### 1. FAISS
+- **Pros**: More index types (IVF, PQ), GPU support
+- **Cons**: Heavier dependency, complex C++ build, less Rust-native
+
+### 2. Annoy (Spotify)
+- **Pros**: Simple, memory-mapped
+- **Cons**: Slower build time, cannot add vectors after build
+
+### 3. Hnswlib
+- **Pros**: Reference HNSW implementation
+- **Cons**: Less maintained, no official Rust bindings
+
+### 4. Custom HNSW Implementation
+- **Pros**: Full control, no external dependency
+- **Cons**: Significant engineering effort, unlikely to match USearch performance
+
+**Decision**: USearch provides the best balance of performance, Rust support, and maintenance.
+
+## Future Extensions
+
+1. **Quantization**: Support int8/binary quantization for reduced memory
+2. **Filtering**: Pre-filtering with predicates before ANN search
+3. **Distributed Index**: Shard vector index across datanodes
+4. **Hybrid Search**: Combine vector similarity with full-text search
+5. **Index Advisor**: Automatic index recommendation based on query patterns
+
+## References
+
+- [USearch GitHub](https://github.com/unum-cloud/usearch)
+- [HNSW Paper](https://arxiv.org/abs/1603.09320)
+- [GreptimeDB Index Architecture](../developer-guide/index-architecture.md)
+- [Puffin Blob Format](../developer-guide/puffin-format.md)