perf(8.0): HNSW removeItem is O(in-degree) via a reverse-adjacency index

removeItem() scanned the ENTIRE corpus on every delete to find nodes that
referenced the removed id (and to repair edges left asymmetric by pruning), so a
delete was O(N) and a bulk delete O(N²) — on the open-core JS vector path that
serves when no native provider is registered.

Maintain a reverse-adjacency index (`target → level → set of nodes that link to
target`), so removeItem touches only the removed node's actual in-neighbors:
O(in-degree) per delete, O(N·degree) for a bulk delete. The index is lazily
built, maintained incrementally at every forward-edge mutation (add-link and
prune), and invalidated (rebuilt on next use) by the bulk paths (cold-load
restore + clear). New tests assert the three invariants that matter for a
reverse index: no dangling references to deleted nodes, the incrementally-
maintained index exactly equals a fresh rebuild from the live adjacency, and
search still returns the survivors' true nearest neighbours (exact vs brute force).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/hnsw/hnswIndex.ts

@@ -32,6 +32,14 @@ const DEFAULT_CONFIG: HNSWConfig = {
  */
 export class JsHnswVectorIndex implements VectorIndexProvider {
   private nouns: Map<string, HNSWNoun> = new Map()
+  /**
+   * Reverse adjacency: `target id → (level → set of node ids that link TO target)`.
+   * Lets `removeItem` find a node's in-neighbors in O(in-degree) instead of scanning
+   * the whole corpus (which made bulk delete O(N²)). Lazily built on first need and
+   * maintained incrementally on link/prune/remove; `null` means "stale — rebuild on
+   * next use" (set by every bulk path: cold-load restore + `clear()`).
+   */
+  private incoming: Map<string, Map<number, Set<string>>> | null = null
   private entryPointId: string | null = null
   private maxLevel = 0
   // Track high-level nodes for O(1) entry point selection
@@ -245,6 +253,9 @@ export class JsHnswVectorIndex implements VectorIndexProvider {
     hnswData: { level: number; connections: Record<string, string[]> },
     noun: HNSWNoun
   ): Promise<void> {
+    // Bulk load sets connections directly (bypassing the link path that maintains
+    // the reverse index) — mark it stale so the next removeItem rebuilds it.
+    this.incoming = null
     const storageWithBlob = this.storage as unknown as {
       loadBinaryBlob?: (key: string) => Promise<Buffer | null>
     }
@@ -489,12 +500,14 @@ export class JsHnswVectorIndex implements VectorIndexProvider {
 
 
         noun.connections.get(level)!.add(neighborId)
+        this.addIncoming(neighborId, level, id) // forward edge id → neighborId
 
         // Add reverse connection
         if (!neighbor.connections.has(level)) {
           neighbor.connections.set(level, new Set<string>())
         }
         neighbor.connections.get(level)!.add(id)
+        this.addIncoming(id, level, neighborId) // forward edge neighborId → id
 
         // Ensure neighbor doesn't have too many connections
         if (neighbor.connections.get(level)!.size > this.config.M) {
@@ -841,6 +854,44 @@ export class JsHnswVectorIndex implements VectorIndexProvider {
     return [...nearestNouns].slice(0, k)
   }
 
+  /**
+   * Build (or return the cached) reverse-adjacency index. O(N + E) the first time
+   * after a bulk load/clear; O(1) thereafter while it stays live.
+   */
+  private ensureIncoming(): Map<string, Map<number, Set<string>>> {
+    if (this.incoming !== null) return this.incoming
+    const inc = new Map<string, Map<number, Set<string>>>()
+    for (const [nodeId, node] of this.nouns) {
+      for (const [level, targets] of node.connections) {
+        for (const target of targets) {
+          let byLevel = inc.get(target)
+          if (!byLevel) { byLevel = new Map(); inc.set(target, byLevel) }
+          let set = byLevel.get(level)
+          if (!set) { set = new Set(); byLevel.set(level, set) }
+          set.add(nodeId)
+        }
+      }
+    }
+    this.incoming = inc
+    return inc
+  }
+
+  /** Record a new forward edge `source → target` at `level` (no-op while the index is stale). */
+  private addIncoming(target: string, level: number, source: string): void {
+    if (this.incoming === null) return
+    let byLevel = this.incoming.get(target)
+    if (!byLevel) { byLevel = new Map(); this.incoming.set(target, byLevel) }
+    let set = byLevel.get(level)
+    if (!set) { set = new Set(); byLevel.set(level, set) }
+    set.add(source)
+  }
+
+  /** Record that the forward edge `source → target` at `level` is gone. */
+  private removeIncoming(target: string, level: number, source: string): void {
+    if (this.incoming === null) return
+    this.incoming.get(target)?.get(level)?.delete(source)
+  }
+
   /**
    * Remove an item from the index
    */
@@ -852,41 +903,38 @@ export class JsHnswVectorIndex implements VectorIndexProvider {
 
     const noun = this.nouns.get(id)!
 
-    // Remove connections to this noun from all neighbors
+    // Reverse-adjacency lets us touch ONLY the nodes that actually reference `id`
-    for (const [level, connections] of noun.connections.entries()) {
+    // (its in-neighbors) rather than scanning the whole corpus — turning a delete
-      for (const neighborId of connections) {
+    // from O(N) into O(in-degree) and a bulk delete from O(N²) into O(N·degree).
-
+    // Snapshot each referrer set because pruneConnections mutates the index.
-        const neighbor = this.nouns.get(neighborId)
+    const incoming = this.ensureIncoming()
-        if (!neighbor) {
+    const referrers = incoming.get(id)
-          // Skip neighbors that don't exist (expected during rapid additions/deletions)
+    if (referrers) {
-          continue
+      for (const [level, refSet] of referrers) {
-        }
+        for (const refId of Array.from(refSet)) {
-        if (neighbor.connections.has(level)) {
+          const ref = this.nouns.get(refId)
-          neighbor.connections.get(level)!.delete(id)
+          if (ref && ref.connections.has(level)) {
-
+            // Drop the forward edge ref → id, then re-prune ref so the graph stays
-          // Prune connections after removing this noun to ensure consistency
+            // navigable. (id's own reverse entry is dropped wholesale below, so we
-          await this.pruneConnections(neighbor, level)
+            // intentionally do not maintain incoming[id] inside this loop.)
+            ref.connections.get(level)!.delete(id)
+            await this.pruneConnections(ref, level)
+          }
         }
       }
     }
 
-    // Also check all other nouns for references to this noun and remove them
+    // id's OUTGOING edges disappear with it → drop id from each out-neighbor's
-    for (const [nounId, otherNoun] of this.nouns.entries()) {
+    // reverse set so no stale referrer survives.
-      if (nounId === id) continue // Skip the noun being removed
+    for (const [level, targets] of noun.connections) {
-
+      for (const target of targets) {
-
+        this.removeIncoming(target, level, id)
-      for (const [level, connections] of otherNoun.connections.entries()) {
-        if (connections.has(id)) {
-          connections.delete(id)
-
-          // Prune connections after removing this reference
-          await this.pruneConnections(otherNoun, level)
-        }
       }
     }
 
-    // Remove the noun
+    // Remove the noun + its reverse-index entry.
     this.nouns.delete(id)
+    this.incoming?.delete(id)
 
     // If we removed the entry point, find a new one
     if (this.entryPointId === id) {
@@ -966,6 +1014,7 @@ export class JsHnswVectorIndex implements VectorIndexProvider {
    */
   public clear(): void {
     this.nouns.clear()
+    this.incoming = null // reverse index no longer reflects the (now empty) graph
     this.entryPointId = null
     this.maxLevel = 0
   }
@@ -1762,7 +1811,11 @@ export class JsHnswVectorIndex implements VectorIndexProvider {
 
     // Only proceed if we have valid neighbors
     if (distances.size === 0) {
-      // If no valid neighbors, clear connections at this level
+      // If no valid neighbors, clear connections at this level. Every current
+      // connection is dropped — unlink each from the reverse index.
+      if (this.incoming !== null) {
+        for (const dropped of connections) this.removeIncoming(dropped, level, noun.id)
+      }
       noun.connections.set(level, new Set())
       return
     }
@@ -1774,8 +1827,16 @@ export class JsHnswVectorIndex implements VectorIndexProvider {
       this.config.M
     )
 
-    // Update connections with only valid neighbors
+    // Update connections with only valid neighbors. Pruning only ever drops
-    noun.connections.set(level, new Set(selectedNeighbors.keys()))
+    // edges (the selected set is a subset of the current connections), so unlink
+    // each dropped neighbor from the reverse index.
+    const kept = new Set(selectedNeighbors.keys())
+    if (this.incoming !== null) {
+      for (const prev of connections) {
+        if (!kept.has(prev)) this.removeIncoming(prev, level, noun.id)
+      }
+    }
+    noun.connections.set(level, kept)
   }
 
   /**

tests/unit/hnsw/remove-reverse-adjacency.test.ts

@@ -0,0 +1,168 @@
+/**
+ * @module tests/unit/hnsw/remove-reverse-adjacency
+ * @description Correctness guard for the reverse-adjacency index that makes
+ * `removeItem` O(in-degree) instead of O(N) (and bulk delete O(N·degree) instead
+ * of O(N²)). The risk of a reverse index is staleness — a missed maintenance site
+ * leaves a dangling reference to a deleted node or a stale referrer. These tests
+ * exercise mixed add/delete workloads and assert three invariants:
+ *
+ *   1. No surviving node's connections reference a deleted id (no dangling edges).
+ *   2. The incrementally-maintained reverse index matches a fresh rebuild from the
+ *      live adjacency — i.e. link/prune/remove maintenance is exactly consistent.
+ *   3. Search still returns the true nearest neighbours of the surviving set
+ *      (verified exactly against a brute-force scan on a complete small graph).
+ */
+import { describe, it, expect, beforeEach } from 'vitest'
+import { JsHnswVectorIndex } from '../../../src/hnsw/hnswIndex.js'
+import { euclideanDistance } from '../../../src/utils/index.js'
+import { MemoryStorage } from '../../../src/storage/adapters/memoryStorage.js'
+
+const DIM = 8
+
+function seededRand(seed: number): () => number {
+  let s = seed >>> 0
+  return () => {
+    s = (s + 0x6d2b79f5) | 0
+    let t = Math.imul(s ^ (s >>> 15), 1 | s)
+    t = (t + Math.imul(t ^ (t >>> 7), 61 | t)) ^ t
+    return ((t ^ (t >>> 14)) >>> 0) / 4294967296
+  }
+}
+
+/** A deterministic vector pointing in a pseudo-random direction (well-connected graph). */
+function vec(idx: number): number[] {
+  const rand = seededRand(idx + 1)
+  return Array.from({ length: DIM }, () => rand() * 2 - 1)
+}
+
+type Noun = { id: string; vector: number[]; connections: Map<number, Set<string>> }
+
+function nounsOf(index: JsHnswVectorIndex): Map<string, Noun> {
+  return (index as unknown as { nouns: Map<string, Noun> }).nouns
+}
+
+/** Flatten a reverse index (or a freshly-derived one) to sorted `target|level|source` triples. */
+function triplesFromIncoming(inc: Map<string, Map<number, Set<string>>>): string[] {
+  const out: string[] = []
+  for (const [target, byLevel] of inc) {
+    for (const [level, sources] of byLevel) {
+      for (const source of sources) out.push(`${target}|${level}|${source}`)
+    }
+  }
+  return out.sort()
+}
+
+/** Derive the ground-truth reverse index directly from the live forward adjacency. */
+function triplesFromAdjacency(nouns: Map<string, Noun>): string[] {
+  const out: string[] = []
+  for (const [nodeId, node] of nouns) {
+    for (const [level, targets] of node.connections) {
+      for (const target of targets) out.push(`${target}|${level}|${nodeId}`)
+    }
+  }
+  return out.sort()
+}
+
+function assertNoDanglingRefs(nouns: Map<string, Noun>): void {
+  for (const [nodeId, node] of nouns) {
+    for (const [level, targets] of node.connections) {
+      for (const target of targets) {
+        expect(nouns.has(target), `node ${nodeId} (L${level}) links to deleted ${target}`).toBe(true)
+      }
+    }
+  }
+}
+
+function assertReverseIndexConsistent(index: JsHnswVectorIndex): void {
+  // ensureIncoming() returns the live (incrementally-maintained) index, building it
+  // only if it was invalidated. The triples it yields must equal the triples derived
+  // straight from the forward adjacency — empty leftover sets contribute nothing.
+  const live = (index as unknown as { ensureIncoming: () => Map<string, Map<number, Set<string>>> }).ensureIncoming()
+  expect(triplesFromIncoming(live)).toEqual(triplesFromAdjacency(nounsOf(index)))
+}
+
+function makeIndex(M: number): JsHnswVectorIndex {
+  return new JsHnswVectorIndex(
+    { M, efConstruction: 200, efSearch: 64, ml: 16 },
+    euclideanDistance,
+    { useParallelization: false, storage: new MemoryStorage() }
+  )
+}
+
+describe('HNSW removeItem — reverse-adjacency correctness', () => {
+  it('leaves no dangling references and a consistent reverse index after interleaved add/delete', async () => {
+    const index = makeIndex(16)
+    const live = new Set<string>()
+
+    // Add 120, then interleave: delete every 3rd as we keep adding — exercises the
+    // incremental maintenance (link + prune on add, unlink on remove) continuously.
+    for (let i = 0; i < 120; i++) {
+      const id = `n-${i}`
+      await index.addItem({ id, vector: vec(i) })
+      live.add(id)
+      if (i % 3 === 0 && i > 0) {
+        const victim = `n-${i - 1}`
+        await index.removeItem(victim)
+        live.delete(victim)
+      }
+    }
+
+    // Now delete ~half of the survivors in one burst (the O(N²)-prone path).
+    const survivors = [...live]
+    for (let i = 0; i < survivors.length; i += 2) {
+      await index.removeItem(survivors[i])
+      live.delete(survivors[i])
+    }
+
+    const nouns = nounsOf(index)
+    expect(nouns.size).toBe(live.size)
+    assertNoDanglingRefs(nouns)
+    assertReverseIndexConsistent(index)
+  })
+
+  it('removing the entry point repeatedly stays consistent', async () => {
+    const index = makeIndex(8)
+    for (let i = 0; i < 40; i++) await index.addItem({ id: `e-${i}`, vector: vec(i) })
+
+    // Delete whatever is currently the entry point, 20 times.
+    for (let k = 0; k < 20; k++) {
+      const ep = (index as unknown as { entryPointId: string | null }).entryPointId
+      if (!ep) break
+      await index.removeItem(ep)
+      assertNoDanglingRefs(nounsOf(index))
+    }
+    assertReverseIndexConsistent(index)
+  })
+
+  it('search returns the true nearest neighbours of the surviving set (exact, complete graph)', async () => {
+    // M ≥ N-1 ⇒ the small graph is complete and never prunes, so HNSW recall is 100%
+    // and we can assert the survivors\' exact top-k against a brute-force scan.
+    const index = makeIndex(64)
+    const all: Array<{ id: string; v: number[] }> = []
+    for (let i = 0; i < 24; i++) {
+      const v = vec(i + 1000)
+      all.push({ id: `s-${i}`, v })
+      await index.addItem({ id: `s-${i}`, vector: v })
+    }
+
+    const deleted = new Set(['s-2', 's-5', 's-9', 's-14', 's-20'])
+    for (const id of deleted) await index.removeItem(id)
+
+    const survivors = all.filter((x) => !deleted.has(x.id))
+    const query = vec(7).map((x) => x * 0.5) // an arbitrary deterministic query point
+    const k = 5
+
+    const bruteTopK = survivors
+      .map((x) => ({ id: x.id, d: euclideanDistance(query, x.v) }))
+      .sort((a, b) => a.d - b.d)
+      .slice(0, k)
+      .map((x) => x.id)
+
+    const got = (await index.search(query, k)).map(([id]) => id)
+
+    expect(got).toEqual(bruteTopK)
+    // And none of the deleted ids can ever surface.
+    expect(got.some((id) => deleted.has(id))).toBe(false)
+    assertNoDanglingRefs(nounsOf(index))
+  })
+})