B-Tree indexing

benchmarks/storage.ts

@@ -49,7 +49,13 @@ function fmtOps(ops: number): string {
 /**
  * Run a full suite of benchmarks against a given storage instance.
  */
-async function benchmarkStorage(label: string, storage: BaseStorage<Doc>, docs: Doc[], supportsRangeOps = true) {
+async function benchmarkStorage(
+  label: string,
+  storage: BaseStorage<Doc>,
+  docs: Doc[],
+  options: { supportsRangeOps?: boolean; hasAgeIndex?: boolean } = {},
+) {
+  const { supportsRangeOps = true, hasAgeIndex = false } = options;
   const count = docs.length;
   console.log(`\n${'='.repeat(60)}`);
   console.log(` ${label}  (${count.toLocaleString()} documents)`);
@@ -85,19 +91,31 @@ async function benchmarkStorage(label: string, storage: BaseStorage<Doc>, docs:
   });
   console.log(`  findOne scan         ${findScanMs.toFixed(2)}ms  (${fmtOps((scanCount / findScanMs) * 1000)} ops/sec)  [${scanCount} lookups]`);
 
-  // --- Find with $gte / $lt range (full scan) ---
+  // --- Range queries ---
   if (supportsRangeOps) {
+    // Wide range: 20% selectivity (10 out of 50 age values).
     const rangeCount = Math.min(count, 100);
-    let rangeTotal = 0;
+    let rangeWideTotal = 0;
-    const findRangeMs = await time(async () => {
+    const findRangeWideMs = await time(async () => {
       for (let i = 0; i < rangeCount; i++) {
         const results = await storage.find({ age: { $gte: 30, $lt: 40 } });
-        rangeTotal += results.length;
+        rangeWideTotal += results.length;
       }
     });
-    console.log(`  find $gte/$lt      ${findRangeMs.toFixed(2)}ms  (${fmtOps((rangeCount / findRangeMs) * 1000)} ops/sec)  [${rangeCount} queries, ~${Math.round(rangeTotal / rangeCount)} hits/query]`);
+    const indexLabel = hasAgeIndex ? 'B+Tree' : 'scan';
+    console.log(`  find wide  [${indexLabel}]  ${findRangeWideMs.toFixed(2)}ms  (${fmtOps((rangeCount / findRangeWideMs) * 1000)} ops/sec)  [${rangeCount}x, ~${Math.round(rangeWideTotal / rangeCount)} hits, 20% sel.]`);
 
-    // --- Find with combined equality + operator (index narrows, operator verifies) ---
+    // Narrow range: 2% selectivity (1 out of 50 age values).
+    let rangeNarrowTotal = 0;
+    const findRangeNarrowMs = await time(async () => {
+      for (let i = 0; i < rangeCount; i++) {
+        const results = await storage.find({ age: { $gte: 42, $lt: 43 } });
+        rangeNarrowTotal += results.length;
+      }
+    });
+    console.log(`  find narrow [${indexLabel}]  ${findRangeNarrowMs.toFixed(2)}ms  (${fmtOps((rangeCount / findRangeNarrowMs) * 1000)} ops/sec)  [${rangeCount}x, ~${Math.round(rangeNarrowTotal / rangeCount)} hits, 2% sel.]`);
+
+    // --- Combined equality + operator ---
     const comboCount = Math.min(count, 1_000);
     const findComboMs = await time(async () => {
       for (let i = 0; i < comboCount; i++) {
@@ -135,7 +153,7 @@ async function benchmarkStorage(label: string, storage: BaseStorage<Doc>, docs:
 // ---------------------------------------------------------------------------
 
 // ---------------------------------------------------------------------------
-// StorageMemory — indexed vs non-indexed
+// StorageMemory — B+ Tree range queries vs full scan
 // ---------------------------------------------------------------------------
 
 const DOC_COUNTS = [1_000, 10_000, 50_000];
@@ -143,46 +161,45 @@ const DOC_COUNTS = [1_000, 10_000, 50_000];
 for (const count of DOC_COUNTS) {
   const docs = generateDocs(count);
 
+  // Indexes on id, name, AND age — range queries on age use B+ Tree.
+  const indexedWithAge = StorageMemory.from<Doc>(['id', 'name', 'age']);
+  await benchmarkStorage('StorageMemory (indexed: id,name,age)', indexedWithAge, docs, { hasAgeIndex: true });
+
+  // Indexes on id, name only — range queries on age fall back to full scan.
   const indexed = StorageMemory.from<Doc>(['id', 'name']);
   await benchmarkStorage('StorageMemory (indexed: id,name)', indexed, docs);
 
+  // No indexes at all.
   const noIndex = StorageMemory.from<Doc>();
   await benchmarkStorage('StorageMemory (no indexes)', noIndex, docs);
 }
 
 // ---------------------------------------------------------------------------
-// EncryptedStorage — with plaintextKeys for range queries
+// EncryptedStorage
 // ---------------------------------------------------------------------------
 
-const ENCRYPTED_DOC_COUNTS = [100, 1_000, 10_000];
+const ENCRYPTED_DOC_COUNTS = [100, 1_000];
 const encryptionKey = await AESKey.fromSeed('benchmark-key');
 
 for (const count of ENCRYPTED_DOC_COUNTS) {
   const docs = generateDocs(count);
 
-  // No indexes + plaintextKeys — range queries on age work.
+  // Indexed + plaintextKeys (age) — range queries on age use B+ Tree via backing store.
-  const encBaseNoIdx = StorageMemory.from<Record<string, any>>();
+  const encBaseA = StorageMemory.from<Record<string, any>>(['id', 'name', 'age']);
-  const encNoIdx = EncryptedStorage.from<Doc>(encBaseNoIdx, encryptionKey, {
-    plaintextKeys: ['age'],
-  });
-  await benchmarkStorage('Encrypted (no indexes, plaintextKeys: age)', encNoIdx, docs);
-
-  // Indexed + plaintextKeys — range queries on age work.
-  const encBaseA = StorageMemory.from<Record<string, any>>(['id', 'name']);
   const encA = EncryptedStorage.from<Doc>(encBaseA, encryptionKey, {
     plaintextKeys: ['age'],
   });
-  await benchmarkStorage('Encrypted (indexed, plaintextKeys: age)', encA, docs);
+  await benchmarkStorage('Encrypted (indexed+age, plaintextKeys: age)', encA, docs, { hasAgeIndex: true });
 
-  // Indexed, fully encrypted — same indexes but no plaintext keys.
+  // Indexed, fully encrypted — no range ops.
   const encBaseB = StorageMemory.from<Record<string, any>>(['id', 'name']);
   const encB = EncryptedStorage.from<Doc>(encBaseB, encryptionKey);
-  await benchmarkStorage('Encrypted (indexed, fully encrypted)', encB, docs, false);
+  await benchmarkStorage('Encrypted (indexed, fully encrypted)', encB, docs, { supportsRangeOps: false });
 
   // No indexes, fully encrypted — worst case.
   const encBaseC = StorageMemory.from<Record<string, any>>();
   const encC = EncryptedStorage.from<Doc>(encBaseC, encryptionKey);
-  await benchmarkStorage('Encrypted (no indexes, fully encrypted)', encC, docs, false);
+  await benchmarkStorage('Encrypted (no indexes, fully encrypted)', encC, docs, { supportsRangeOps: false });
 }
 
 console.log('\nDone.\n');

src/storage/storage-localstorage.ts

@@ -6,6 +6,7 @@ import {
   type ComparisonOperators,
   isOperatorObject,
 } from './base-storage.js';
+import { BPlusTree, type BPlusTreeEntry } from 'src/utils/btree.js';
 
 /**
  * Key prefix separator used to namespace documents within localStorage.
@@ -25,7 +26,7 @@ const MANIFEST_SUFFIX = '__keys__';
 const COUNTER_SUFFIX = '__next__';
 
 /**
- * Separator used when joining multiple field values into a single index key.
+ * Separator used when joining field names to create the index map key.
  */
 const INDEX_KEY_SEP = '\x00';
 
@@ -41,6 +42,18 @@ function normalizeIndexes(indexes?: IndexDefinition): string[][] {
   return indexes as string[][];
 }
 
+/**
+ * Comparator for compound index keys (arrays of raw values).
+ */
+function tupleCompare(a: any[], b: any[]): number {
+  const len = Math.min(a.length, b.length);
+  for (let i = 0; i < len; i++) {
+    if (a[i] < b[i]) return -1;
+    if (a[i] > b[i]) return 1;
+  }
+  return a.length - b.length;
+}
+
 /**
  * Implementation of BaseStorage using the browser's localStorage API.
  *
@@ -50,9 +63,9 @@ function normalizeIndexes(indexes?: IndexDefinition): string[][] {
  * tracks all internal keys so that read operations avoid scanning every
  * key in localStorage.
  *
- * Optional indexes provide fast lookups when a query filter matches
+ * Optional indexes are backed by B+ Trees, providing O(log n) equality
- * an index exactly. Indexes are held in memory and rebuilt only when a
+ * lookups and O(log n + k) range queries. Indexes are held in memory and
- * cross-tab manifest change is detected.
+ * rebuilt only when a cross-tab manifest change is detected.
  *
  * Because localStorage is synchronous and string-only, all values are
  * JSON-serialised on write and parsed on read.
@@ -91,12 +104,11 @@ export class StorageLocalStorage<
   private indexDefs: string[][];
 
   /**
-   * Secondary index maps (same structure as StorageMemory).
+   * Secondary indexes backed by B+ Trees.
-   * Outer key  = index name (joined field names).
+   * Map key = index name (joined field names).
-   * Inner key  = index value (joined field values from a document).
+   * Map value = B+ Tree mapping index keys to sets of internal document keys.
-   * Inner value = set of internal numeric keys.
    */
-  private indexes: Map<string, Map<string, Set<number>>>;
+  private indexes: Map<string, BPlusTree<any, number>>;
 
   /** Lazily-created child storage instances. */
   private children: Map<string, StorageLocalStorage<any>>;
@@ -111,7 +123,9 @@ export class StorageLocalStorage<
     this.indexDefs = normalizeIndexes(indexes);
     this.indexes = new Map();
     for (const fields of this.indexDefs) {
-      this.indexes.set(fields.join(INDEX_KEY_SEP), new Map());
+      const name = fields.join(INDEX_KEY_SEP);
+      const comparator = fields.length > 1 ? tupleCompare : undefined;
+      this.indexes.set(name, new BPlusTree<any, number>(32, comparator));
     }
 
     // Bootstrap from localStorage.
@@ -143,19 +157,21 @@ export class StorageLocalStorage<
     this.refreshManifest();
 
     let results: T[];
-    const indexedKeys = this.resolveIndexKeys(filter);
+    const resolution = this.resolveIndexKeys(filter);
+
+    if (resolution !== null) {
+      const { keys, resolvedFields } = resolution;
+      const filterKeys = filter ? Object.keys(filter) : [];
+      const needsVerification = filterKeys.some((k) => !resolvedFields.includes(k));
 
-    if (indexedKeys !== null) {
-      // Use the index to narrow which documents we read from localStorage.
       results = [];
-      for (const key of indexedKeys) {
+      for (const key of keys) {
         const raw = localStorage.getItem(this.docKey(key));
         if (raw === null) continue;
         const doc = JSON.parse(raw) as T;
-        if (this.matchesFilter(doc, filter)) {
+        if (needsVerification && !this.matchesFilter(doc, filter)) continue;
         results.push(doc);
       }
-      }
     } else {
       // Full scan over all documents in the manifest.
       results = [];
@@ -290,11 +306,23 @@ export class StorageLocalStorage<
    * Uses an index when possible, otherwise falls back to a full scan.
    */
   private collectMatches(filter?: Filter<T>): Array<[number, T]> {
-    const indexKeys = this.resolveIndexKeys(filter);
+    const resolution = this.resolveIndexKeys(filter);
-    const keysToScan = indexKeys ?? this.manifest;
     const results: Array<[number, T]> = [];
 
-    for (const key of keysToScan) {
+    if (resolution !== null) {
+      const { keys, resolvedFields } = resolution;
+      const filterKeys = filter ? Object.keys(filter) : [];
+      const needsVerification = filterKeys.some((k) => !resolvedFields.includes(k));
+
+      for (const key of keys) {
+        const raw = localStorage.getItem(this.docKey(key));
+        if (raw === null) continue;
+        const doc = JSON.parse(raw) as T;
+        if (needsVerification && !this.matchesFilter(doc, filter)) continue;
+        results.push([key, doc]);
+      }
+    } else {
+      for (const key of this.manifest) {
         const raw = localStorage.getItem(this.docKey(key));
         if (raw === null) continue;
         const doc = JSON.parse(raw) as T;
@@ -302,6 +330,7 @@ export class StorageLocalStorage<
           results.push([key, doc]);
         }
       }
+    }
 
     return results;
   }
@@ -325,48 +354,44 @@ export class StorageLocalStorage<
   // ---------------------------------------------------------------------------
 
   /**
-   * Build the index value string for a given document and set of fields.
+   * Build the B+ Tree key for a document and a set of index fields.
-   * Returns `null` if any field is missing from the document.
+   * - Single-field indexes return the raw field value.
+   * - Compound indexes return an array of raw field values.
+   * Returns `null` if any required field is missing from the document.
    */
-  private buildIndexValue(doc: Record<string, any>, fields: string[]): string | null {
+  private buildIndexKey(doc: Record<string, any>, fields: string[]): any | null {
-    const parts: string[] = [];
+    if (fields.length === 1) {
+      if (!(fields[0] in doc)) return null;
+      return doc[fields[0]];
+    }
+
+    const parts: any[] = [];
     for (const field of fields) {
       if (!(field in doc)) return null;
-      parts.push(String(doc[field]));
+      parts.push(doc[field]);
     }
-    return parts.join(INDEX_KEY_SEP);
+    return parts;
   }
 
   /** Register a document in all applicable indexes. */
   private addToIndexes(internalKey: number, doc: T): void {
     for (const fields of this.indexDefs) {
-      const indexName = fields.join(INDEX_KEY_SEP);
+      const indexKey = this.buildIndexKey(doc, fields);
-      const indexValue = this.buildIndexValue(doc, fields);
+      if (indexKey === null) continue;
-      if (indexValue === null) continue;
 
-      const indexMap = this.indexes.get(indexName)!;
+      const name = fields.join(INDEX_KEY_SEP);
-      let bucket = indexMap.get(indexValue);
+      this.indexes.get(name)!.insert(indexKey, internalKey);
-      if (!bucket) {
-        bucket = new Set();
-        indexMap.set(indexValue, bucket);
-      }
-      bucket.add(internalKey);
     }
   }
 
   /** Remove a document from all applicable indexes. */
   private removeFromIndexes(internalKey: number, doc: T): void {
     for (const fields of this.indexDefs) {
-      const indexName = fields.join(INDEX_KEY_SEP);
+      const indexKey = this.buildIndexKey(doc, fields);
-      const indexValue = this.buildIndexValue(doc, fields);
+      if (indexKey === null) continue;
-      if (indexValue === null) continue;
 
-      const indexMap = this.indexes.get(indexName)!;
+      const name = fields.join(INDEX_KEY_SEP);
-      const bucket = indexMap.get(indexValue);
+      this.indexes.get(name)!.delete(indexKey, internalKey);
-      if (bucket) {
-        bucket.delete(internalKey);
-        if (bucket.size === 0) indexMap.delete(indexValue);
-      }
     }
   }
 
@@ -374,45 +399,104 @@ export class StorageLocalStorage<
    * Attempt to resolve candidate internal keys from the indexes.
    * Returns `null` if no index can serve the query.
    *
-   * Only plain equality values are used for index resolution — operator
+   * Supports three resolution strategies:
-   * objects are excluded since hash-based indexes only support equality.
+   * 1. Equality lookup via B+ Tree `.get()` — O(log n)
+   * 2. Range scan via B+ Tree `.range()` — O(log n + k)
+   * 3. Compound equality — B+ Tree `.get()` with a tuple key
    */
-  private resolveIndexKeys(filter?: Filter<T>): Set<number> | null {
+  private resolveIndexKeys(
+    filter?: Filter<T>,
+  ): { keys: Iterable<number>; resolvedFields: string[] } | null {
     if (!filter) return null;
     const filterKeys = Object.keys(filter);
     if (filterKeys.length === 0) return null;
 
-    const equalityFilter: Record<string, any> = {};
-    for (const [key, value] of Object.entries(filter)) {
-      if (!isOperatorObject(value)) {
-        equalityFilter[key] = value;
-      }
-    }
-
-    if (Object.keys(equalityFilter).length === 0) return null;
-
     for (const fields of this.indexDefs) {
-      if (!fields.every((f) => f in equalityFilter)) continue;
-
       const indexName = fields.join(INDEX_KEY_SEP);
-      const indexValue = this.buildIndexValue(equalityFilter, fields);
+      const btree = this.indexes.get(indexName)!;
-      if (indexValue === null) continue;
 
-      const indexMap = this.indexes.get(indexName)!;
+      if (fields.length === 1) {
-      const bucket = indexMap.get(indexValue);
+        // --- Single-field index ---
-      return bucket ?? new Set();
+        const field = fields[0];
+        if (!(field in filter)) continue;
+
+        const filterValue = (filter as any)[field];
+
+        if (isOperatorObject(filterValue)) {
+          const keys = this.resolveOperatorViaTree(btree, filterValue);
+          if (keys !== null) return { keys, resolvedFields: [field] };
+          continue;
+        }
+
+        // Plain equality.
+        return { keys: btree.get(filterValue) ?? [], resolvedFields: [field] };
+      } else {
+        // --- Compound index — all fields must be plain equality ---
+        if (!fields.every((f) => f in filter && !isOperatorObject((filter as any)[f]))) {
+          continue;
+        }
+
+        const tupleKey = fields.map((f) => (filter as any)[f]);
+        return { keys: btree.get(tupleKey) ?? [], resolvedFields: [...fields] };
+      }
     }
 
     return null;
   }
 
   /**
-   * Rebuild all in-memory index maps by reading every document from
+   * Try to resolve an operator filter against a single-field B+ Tree index.
+   * Returns a flat array of matching internal keys, or null if the
+   * operators can't be served by the tree ($ne).
+   */
+  private resolveOperatorViaTree(
+    btree: BPlusTree<any, number>,
+    ops: ComparisonOperators<any>,
+  ): Iterable<number> | null {
+    if (ops.$ne !== undefined) return null;
+
+    if (ops.$eq !== undefined) {
+      return btree.get(ops.$eq) ?? [];
+    }
+
+    let min: any = undefined;
+    let max: any = undefined;
+    let lowerInclusive = true;
+    let upperInclusive = false;
+
+    if (ops.$gt !== undefined) { min = ops.$gt; lowerInclusive = false; }
+    if (ops.$gte !== undefined) { min = ops.$gte; lowerInclusive = true; }
+    if (ops.$lt !== undefined) { max = ops.$lt; upperInclusive = false; }
+    if (ops.$lte !== undefined) { max = ops.$lte; upperInclusive = true; }
+
+    if (min === undefined && max === undefined) return null;
+
+    const entries = btree.range(min, max, { lowerInclusive, upperInclusive });
+    return this.flattenEntryKeys(entries);
+  }
+
+  /**
+   * Flatten B+ Tree range results into a flat array of internal keys.
+   * Uses an array instead of a Set — no hash overhead, no deduplication
+   * needed because each internal key only appears under one index key.
+   */
+  private flattenEntryKeys(entries: BPlusTreeEntry<any, number>[]): number[] {
+    const result: number[] = [];
+    for (const entry of entries) {
+      for (const key of entry.values) {
+        result.push(key);
+      }
+    }
+    return result;
+  }
+
+  /**
+   * Rebuild all in-memory index B+ Trees by reading every document from
    * localStorage. Called only when a cross-tab manifest change is detected.
    */
   private rebuildIndexes(): void {
-    for (const [, indexMap] of this.indexes) {
+    for (const [, btree] of this.indexes) {
-      indexMap.clear();
+      btree.clear();
     }
 
     for (const key of this.manifest) {

src/storage/storage-memory.ts

@@ -6,10 +6,10 @@ import {
   type ComparisonOperators,
   isOperatorObject,
 } from './base-storage.js';
+import { BPlusTree, type BPlusTreeEntry } from 'src/utils/btree.js';
 
 /**
- * Separator used when joining multiple field values into a single index key.
+ * Separator used when joining field names to create the index map key.
- * Chosen to be unlikely to appear in real field values.
  */
 const INDEX_KEY_SEP = '\x00';
 
@@ -29,13 +29,26 @@ function normalizeIndexes(indexes?: IndexDefinition): string[][] {
   return indexes as string[][];
 }
 
+/**
+ * Comparator for compound index keys (arrays of raw values).
+ * Compares element-by-element using native `<` / `>` operators.
+ */
+function tupleCompare(a: any[], b: any[]): number {
+  const len = Math.min(a.length, b.length);
+  for (let i = 0; i < len; i++) {
+    if (a[i] < b[i]) return -1;
+    if (a[i] > b[i]) return 1;
+  }
+  return a.length - b.length;
+}
+
 /**
  * Implementation of BaseStore using Memory as the storage backend.
  *
  * @remarks
  * Documents are keyed internally by an auto-incrementing numeric key.
- * Optional indexes provide O(1) lookups when a query filter matches
+ * Optional indexes are backed by B+ Trees, providing O(log n) equality
- * an index exactly.
+ * lookups and O(log n + k) range queries.
  */
 export class StorageMemory<
   T extends Record<string, any> = Record<string, any>,
@@ -53,12 +66,11 @@ export class StorageMemory<
   private store: Map<number, T>;
 
   /**
-   * Secondary index maps.
+   * Secondary indexes backed by B+ Trees.
-   * Outer key  = index name (joined field names).
+   * Map key = index name (joined field names).
-   * Inner key  = index value (joined field values from a document).
+   * Map value = B+ Tree mapping index keys to sets of internal document keys.
-   * Inner value = set of internal keys that share this index value.
    */
-  private indexes: Map<string, Map<string, Set<number>>>;
+  private indexes: Map<string, BPlusTree<any, number>>;
 
   /** The normalized index definitions supplied at construction time. */
   private indexDefs: string[][];
@@ -73,10 +85,12 @@ export class StorageMemory<
     this.children = new Map();
     this.indexDefs = normalizeIndexes(indexes);
 
-    // Initialise an empty map for each index definition.
+    // Create a B+ Tree for each index definition.
     this.indexes = new Map();
     for (const fields of this.indexDefs) {
-      this.indexes.set(fields.join(INDEX_KEY_SEP), new Map());
+      const name = fields.join(INDEX_KEY_SEP);
+      const comparator = fields.length > 1 ? tupleCompare : undefined;
+      this.indexes.set(name, new BPlusTree<any, number>(32, comparator));
     }
   }
 
@@ -225,17 +239,20 @@ export class StorageMemory<
    * Uses an index when possible, otherwise falls back to a full scan.
    */
   private collectMatches(filter?: Filter<T>): Array<[number, T]> {
-    const indexKeys = this.resolveIndexKeys(filter);
+    const resolution = this.resolveIndexKeys(filter);
+
+    if (resolution !== null) {
+      const { keys, resolvedFields } = resolution;
+      const filterKeys = filter ? Object.keys(filter) : [];
+      const needsVerification = filterKeys.some((k) => !resolvedFields.includes(k));
 
-    if (indexKeys !== null) {
-      // We have candidate internal keys from the index — fetch and verify.
       const results: Array<[number, T]> = [];
-      for (const key of indexKeys) {
+      for (const key of keys) {
         const doc = this.store.get(key);
-        if (doc && this.matchesFilter(doc, filter)) {
+        if (!doc) continue;
+        if (needsVerification && !this.matchesFilter(doc, filter)) continue;
         results.push([key, doc]);
       }
-      }
       return results;
     }
 
@@ -269,107 +286,166 @@ export class StorageMemory<
   // ---------------------------------------------------------------------------
 
   /**
-   * Build the index value string for a given document and set of fields.
+   * Build the B+ Tree key for a document and a set of index fields.
-   * Returns `null` if any of the fields are missing from the document,
+   * - Single-field indexes return the raw field value.
-   * since we can't meaningfully index a partial key.
+   * - Compound indexes return an array of raw field values.
+   * Returns `null` if any required field is missing from the document.
    */
-  private buildIndexValue(doc: Record<string, any>, fields: string[]): string | null {
+  private buildIndexKey(doc: Record<string, any>, fields: string[]): any | null {
-    const parts: string[] = [];
+    if (fields.length === 1) {
+      if (!(fields[0] in doc)) return null;
+      return doc[fields[0]];
+    }
+
+    const parts: any[] = [];
     for (const field of fields) {
       if (!(field in doc)) return null;
-      parts.push(String(doc[field]));
+      parts.push(doc[field]);
     }
-    return parts.join(INDEX_KEY_SEP);
+    return parts;
   }
 
   /** Register a document in all applicable indexes. */
   private addToIndexes(internalKey: number, doc: T): void {
     for (const fields of this.indexDefs) {
-      const indexName = fields.join(INDEX_KEY_SEP);
+      const indexKey = this.buildIndexKey(doc, fields);
-      const indexValue = this.buildIndexValue(doc, fields);
+      if (indexKey === null) continue;
-      if (indexValue === null) continue;
 
-      const indexMap = this.indexes.get(indexName)!;
+      const name = fields.join(INDEX_KEY_SEP);
-      let bucket = indexMap.get(indexValue);
+      this.indexes.get(name)!.insert(indexKey, internalKey);
-      if (!bucket) {
-        bucket = new Set();
-        indexMap.set(indexValue, bucket);
-      }
-      bucket.add(internalKey);
     }
   }
 
   /** Remove a document from all applicable indexes. */
   private removeFromIndexes(internalKey: number, doc: T): void {
     for (const fields of this.indexDefs) {
-      const indexName = fields.join(INDEX_KEY_SEP);
+      const indexKey = this.buildIndexKey(doc, fields);
-      const indexValue = this.buildIndexValue(doc, fields);
+      if (indexKey === null) continue;
-      if (indexValue === null) continue;
 
-      const indexMap = this.indexes.get(indexName)!;
+      const name = fields.join(INDEX_KEY_SEP);
-      const bucket = indexMap.get(indexValue);
+      this.indexes.get(name)!.delete(indexKey, internalKey);
-      if (bucket) {
-        bucket.delete(internalKey);
-        if (bucket.size === 0) indexMap.delete(indexValue);
-      }
     }
   }
 
   /**
-   * Attempt to resolve a set of candidate internal keys from the indexes.
+   * Result of an index resolution attempt.
-   * Returns `null` if no index can serve the query.
+   * `keys` is an iterable of candidate internal keys.
-   *
+   * `resolvedFields` lists the filter fields fully satisfied by the index,
-   * An index is used when the filter contains plain equality values for every
+   * so callers can skip re-verifying those conditions in matchesFilter.
-   * field in the index. Operator objects (e.g. `{ $lt: 50 }`) are excluded
-   * from index resolution since hash-based indexes only support equality.
    */
-  private resolveIndexKeys(filter?: Filter<T>): Set<number> | null {
+  private resolveIndexKeys(
+    filter?: Filter<T>,
+  ): { keys: Iterable<number>; resolvedFields: string[] } | null {
     if (!filter) return null;
     const filterKeys = Object.keys(filter);
     if (filterKeys.length === 0) return null;
 
-    // Extract only the equality fields from the filter (skip operator objects).
-    const equalityFilter: Record<string, any> = {};
-    for (const [key, value] of Object.entries(filter)) {
-      if (!isOperatorObject(value)) {
-        equalityFilter[key] = value;
-      }
-    }
-
-    if (Object.keys(equalityFilter).length === 0) return null;
-
     for (const fields of this.indexDefs) {
-      // Every field in the index must be present as an equality value.
-      if (!fields.every((f) => f in equalityFilter)) continue;
-
       const indexName = fields.join(INDEX_KEY_SEP);
-      const indexValue = this.buildIndexValue(equalityFilter, fields);
+      const btree = this.indexes.get(indexName)!;
-      if (indexValue === null) continue;
 
-      const indexMap = this.indexes.get(indexName)!;
+      if (fields.length === 1) {
-      const bucket = indexMap.get(indexValue);
+        // --- Single-field index ---
-      return bucket ?? new Set();
+        const field = fields[0];
+        if (!(field in filter)) continue;
+
+        const filterValue = (filter as any)[field];
+
+        if (isOperatorObject(filterValue)) {
+          const keys = this.resolveOperatorViaTree(btree, filterValue);
+          if (keys !== null) return { keys, resolvedFields: [field] };
+          continue;
+        }
+
+        // Plain equality.
+        return { keys: btree.get(filterValue) ?? [], resolvedFields: [field] };
+      } else {
+        // --- Compound index — all fields must be plain equality ---
+        if (!fields.every((f) => f in filter && !isOperatorObject((filter as any)[f]))) {
+          continue;
+        }
+
+        const tupleKey = fields.map((f) => (filter as any)[f]);
+        return { keys: btree.get(tupleKey) ?? [], resolvedFields: [...fields] };
+      }
     }
 
     return null;
   }
 
+  /**
+   * Try to resolve an operator filter against a single-field B+ Tree index.
+   * Returns a flat array of matching internal keys, or null if the
+   * operators can't be served by the tree ($ne).
+   */
+  private resolveOperatorViaTree(
+    btree: BPlusTree<any, number>,
+    ops: ComparisonOperators<any>,
+  ): Iterable<number> | null {
+    // $ne prevents efficient index use.
+    if (ops.$ne !== undefined) return null;
+
+    // $eq is a point lookup.
+    if (ops.$eq !== undefined) {
+      return btree.get(ops.$eq) ?? [];
+    }
+
+    // Extract range bounds from the remaining operators.
+    let min: any = undefined;
+    let max: any = undefined;
+    let lowerInclusive = true;
+    let upperInclusive = false;
+
+    if (ops.$gt !== undefined) { min = ops.$gt; lowerInclusive = false; }
+    if (ops.$gte !== undefined) { min = ops.$gte; lowerInclusive = true; }
+    if (ops.$lt !== undefined) { max = ops.$lt; upperInclusive = false; }
+    if (ops.$lte !== undefined) { max = ops.$lte; upperInclusive = true; }
+
+    if (min === undefined && max === undefined) return null;
+
+    const entries = btree.range(min, max, { lowerInclusive, upperInclusive });
+    return this.flattenEntryKeys(entries);
+  }
+
+  /**
+   * Flatten B+ Tree range results into a flat array of internal keys.
+   * Uses an array instead of a Set — no hash overhead, no deduplication
+   * needed because each internal key only appears under one index key.
+   */
+  private flattenEntryKeys(entries: BPlusTreeEntry<any, number>[]): number[] {
+    const result: number[] = [];
+    for (const entry of entries) {
+      for (const key of entry.values) {
+        result.push(key);
+      }
+    }
+    return result;
+  }
+
   /**
    * Try to answer a `find` query entirely through an index.
    * Returns `null` when no index can serve the filter, signalling
    * the caller to fall back to a full scan.
+   *
+   * When the index covers every field in the filter, matchesFilter
+   * is skipped entirely — the B+ Tree has already ensured the
+   * conditions are met.
    */
   private findViaIndex(filter?: Filter<T>): T[] | null {
-    const keys = this.resolveIndexKeys(filter);
+    const resolution = this.resolveIndexKeys(filter);
-    if (keys === null) return null;
+    if (resolution === null) return null;
+
+    const { keys, resolvedFields } = resolution;
+    const filterKeys = filter ? Object.keys(filter) : [];
+    const needsVerification = filterKeys.some((k) => !resolvedFields.includes(k));
 
     const results: T[] = [];
     for (const key of keys) {
       const doc = this.store.get(key);
-      if (doc && this.matchesFilter(doc, filter)) {
+      if (!doc) continue;
+      if (needsVerification && !this.matchesFilter(doc, filter)) continue;
       results.push(doc);
     }
-    }
     return results;
   }
 }

src/utils/btree.test.ts

@@ -0,0 +1,391 @@
+import { describe, it, expect, beforeEach } from 'vitest';
+import { BPlusTree } from './btree.js';
+
+describe('BPlusTree', () => {
+  let tree: BPlusTree<number, string>;
+
+  beforeEach(() => {
+    tree = new BPlusTree<number, string>();
+  });
+
+  // -------------------------------------------------------------------------
+  // Construction
+  // -------------------------------------------------------------------------
+
+  describe('constructor', () => {
+    it('should create an empty tree', () => {
+      expect(tree.size).toBe(0);
+    });
+
+    it('should reject order < 3', () => {
+      expect(() => new BPlusTree(2)).toThrow('order must be at least 3');
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // Insert & Get
+  // -------------------------------------------------------------------------
+
+  describe('insert and get', () => {
+    it('should insert and retrieve a single entry', () => {
+      tree.insert(10, 'a');
+      expect(tree.get(10)).toEqual(new Set(['a']));
+      expect(tree.size).toBe(1);
+    });
+
+    it('should handle multiple distinct keys', () => {
+      tree.insert(10, 'a');
+      tree.insert(20, 'b');
+      tree.insert(5, 'c');
+      expect(tree.get(10)).toEqual(new Set(['a']));
+      expect(tree.get(20)).toEqual(new Set(['b']));
+      expect(tree.get(5)).toEqual(new Set(['c']));
+      expect(tree.size).toBe(3);
+    });
+
+    it('should return undefined for missing keys', () => {
+      tree.insert(10, 'a');
+      expect(tree.get(99)).toBeUndefined();
+    });
+
+    it('should accumulate duplicate keys into a Set', () => {
+      tree.insert(10, 'a');
+      tree.insert(10, 'b');
+      tree.insert(10, 'c');
+      expect(tree.get(10)).toEqual(new Set(['a', 'b', 'c']));
+      expect(tree.size).toBe(3);
+    });
+
+    it('should not double-count duplicate values for the same key', () => {
+      tree.insert(10, 'a');
+      tree.insert(10, 'a');
+      expect(tree.get(10)).toEqual(new Set(['a']));
+      expect(tree.size).toBe(1);
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // Delete
+  // -------------------------------------------------------------------------
+
+  describe('delete', () => {
+    it('should delete a specific value from a key', () => {
+      tree.insert(10, 'a');
+      tree.insert(10, 'b');
+      expect(tree.delete(10, 'a')).toBe(true);
+      expect(tree.get(10)).toEqual(new Set(['b']));
+      expect(tree.size).toBe(1);
+    });
+
+    it('should remove the key entry when its last value is deleted', () => {
+      tree.insert(10, 'a');
+      expect(tree.delete(10, 'a')).toBe(true);
+      expect(tree.get(10)).toBeUndefined();
+      expect(tree.size).toBe(0);
+    });
+
+    it('should delete all values for a key when value is omitted', () => {
+      tree.insert(10, 'a');
+      tree.insert(10, 'b');
+      expect(tree.delete(10)).toBe(true);
+      expect(tree.get(10)).toBeUndefined();
+      expect(tree.size).toBe(0);
+    });
+
+    it('should return false for non-existent key', () => {
+      expect(tree.delete(99)).toBe(false);
+    });
+
+    it('should return false for non-existent value', () => {
+      tree.insert(10, 'a');
+      expect(tree.delete(10, 'z')).toBe(false);
+      expect(tree.size).toBe(1);
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // Range queries
+  // -------------------------------------------------------------------------
+
+  describe('range', () => {
+    beforeEach(() => {
+      for (let i = 0; i < 100; i++) {
+        tree.insert(i, `v${i}`);
+      }
+    });
+
+    it('should return all entries when no bounds given', () => {
+      const result = tree.range();
+      expect(result.length).toBe(100);
+      expect(result[0].key).toBe(0);
+      expect(result[99].key).toBe(99);
+    });
+
+    it('should return entries in key order', () => {
+      const keys = tree.range().map((e) => e.key);
+      for (let i = 1; i < keys.length; i++) {
+        expect(keys[i]).toBeGreaterThan(keys[i - 1]);
+      }
+    });
+
+    it('should respect lower bound (inclusive by default)', () => {
+      const result = tree.range(50);
+      expect(result.length).toBe(50);
+      expect(result[0].key).toBe(50);
+    });
+
+    it('should respect upper bound (exclusive by default)', () => {
+      const result = tree.range(undefined, 10);
+      expect(result.length).toBe(10);
+      expect(result[result.length - 1].key).toBe(9);
+    });
+
+    it('should support inclusive upper bound', () => {
+      const result = tree.range(undefined, 10, { upperInclusive: true });
+      expect(result.length).toBe(11);
+      expect(result[result.length - 1].key).toBe(10);
+    });
+
+    it('should support exclusive lower bound', () => {
+      const result = tree.range(50, undefined, { lowerInclusive: false });
+      expect(result.length).toBe(49);
+      expect(result[0].key).toBe(51);
+    });
+
+    it('should handle combined bounds', () => {
+      const result = tree.range(20, 30);
+      expect(result.length).toBe(10);
+      expect(result[0].key).toBe(20);
+      expect(result[result.length - 1].key).toBe(29);
+    });
+
+    it('should return empty array for no-result range', () => {
+      const result = tree.range(200, 300);
+      expect(result).toEqual([]);
+    });
+
+    it('should return empty for inverted bounds', () => {
+      const result = tree.range(50, 10);
+      expect(result).toEqual([]);
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // Edge cases
+  // -------------------------------------------------------------------------
+
+  describe('edge cases', () => {
+    it('should handle get on empty tree', () => {
+      expect(tree.get(1)).toBeUndefined();
+    });
+
+    it('should handle range on empty tree', () => {
+      expect(tree.range()).toEqual([]);
+    });
+
+    it('should handle delete on empty tree', () => {
+      expect(tree.delete(1)).toBe(false);
+    });
+
+    it('should handle insert-then-delete-all back to empty', () => {
+      for (let i = 0; i < 50; i++) {
+        tree.insert(i, `v${i}`);
+      }
+      for (let i = 0; i < 50; i++) {
+        expect(tree.delete(i, `v${i}`)).toBe(true);
+      }
+      expect(tree.size).toBe(0);
+      expect(tree.range()).toEqual([]);
+      // Verify we can still insert after emptying.
+      tree.insert(1, 'new');
+      expect(tree.get(1)).toEqual(new Set(['new']));
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // Clear
+  // -------------------------------------------------------------------------
+
+  describe('clear', () => {
+    it('should reset the tree to empty', () => {
+      for (let i = 0; i < 100; i++) tree.insert(i, `v${i}`);
+      expect(tree.size).toBe(100);
+      tree.clear();
+      expect(tree.size).toBe(0);
+      expect(tree.get(0)).toBeUndefined();
+      expect(tree.range()).toEqual([]);
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // Entries iterator
+  // -------------------------------------------------------------------------
+
+  describe('entries', () => {
+    it('should yield all entries in key order', () => {
+      tree.insert(30, 'c');
+      tree.insert(10, 'a');
+      tree.insert(20, 'b');
+
+      const result = [...tree.entries()];
+      expect(result.map((e) => e.key)).toEqual([10, 20, 30]);
+    });
+
+    it('should yield nothing for empty tree', () => {
+      expect([...tree.entries()]).toEqual([]);
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // Large dataset
+  // -------------------------------------------------------------------------
+
+  describe('large dataset', () => {
+    const N = 10_000;
+
+    it('should correctly store and retrieve N items', () => {
+      for (let i = 0; i < N; i++) {
+        tree.insert(i, `v${i}`);
+      }
+      expect(tree.size).toBe(N);
+
+      // Spot-check some values.
+      expect(tree.get(0)).toEqual(new Set(['v0']));
+      expect(tree.get(N - 1)).toEqual(new Set([`v${N - 1}`]));
+      expect(tree.get(Math.floor(N / 2))).toEqual(new Set([`v${Math.floor(N / 2)}`]));
+    });
+
+    it('should produce correct range results on large dataset', () => {
+      for (let i = 0; i < N; i++) {
+        tree.insert(i, `v${i}`);
+      }
+
+      const result = tree.range(5000, 5010);
+      expect(result.length).toBe(10);
+      expect(result[0].key).toBe(5000);
+      expect(result[9].key).toBe(5009);
+    });
+
+    it('should survive inserting and deleting many items', () => {
+      for (let i = 0; i < N; i++) {
+        tree.insert(i, `v${i}`);
+      }
+
+      // Delete the first half.
+      for (let i = 0; i < N / 2; i++) {
+        expect(tree.delete(i, `v${i}`)).toBe(true);
+      }
+
+      expect(tree.size).toBe(N / 2);
+      expect(tree.get(0)).toBeUndefined();
+      expect(tree.get(N / 2)).toEqual(new Set([`v${N / 2}`]));
+
+      // Remaining range should start at N/2.
+      const remaining = tree.range();
+      expect(remaining.length).toBe(N / 2);
+      expect(remaining[0].key).toBe(N / 2);
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // Custom comparator
+  // -------------------------------------------------------------------------
+
+  describe('custom comparator', () => {
+    it('should support reverse ordering', () => {
+      const reverseTree = new BPlusTree<number, string>(32, (a, b) => b - a);
+      reverseTree.insert(1, 'a');
+      reverseTree.insert(2, 'b');
+      reverseTree.insert(3, 'c');
+
+      const entries = [...reverseTree.entries()];
+      expect(entries.map((e) => e.key)).toEqual([3, 2, 1]);
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // Node splitting (small order to force splits)
+  // -------------------------------------------------------------------------
+
+  describe('node splitting with small order', () => {
+    let smallTree: BPlusTree<number, string>;
+
+    beforeEach(() => {
+      smallTree = new BPlusTree<number, string>(4);
+    });
+
+    it('should handle splits correctly', () => {
+      // Order 4 means max 3 keys per node — splits after the 4th insert.
+      for (let i = 0; i < 20; i++) {
+        smallTree.insert(i, `v${i}`);
+      }
+      expect(smallTree.size).toBe(20);
+
+      // All values should be retrievable.
+      for (let i = 0; i < 20; i++) {
+        expect(smallTree.get(i)).toEqual(new Set([`v${i}`]));
+      }
+    });
+
+    it('should maintain sorted order after many splits', () => {
+      // Insert in random order to stress split logic.
+      const values = Array.from({ length: 50 }, (_, i) => i);
+      for (let i = values.length - 1; i > 0; i--) {
+        const j = Math.floor(Math.random() * (i + 1));
+        [values[i], values[j]] = [values[j], values[i]];
+      }
+
+      for (const v of values) {
+        smallTree.insert(v, `v${v}`);
+      }
+
+      const entries = [...smallTree.entries()];
+      const keys = entries.map((e) => e.key);
+      expect(keys).toEqual([...keys].sort((a, b) => a - b));
+    });
+
+    it('should handle delete with merging at small order', () => {
+      for (let i = 0; i < 20; i++) {
+        smallTree.insert(i, `v${i}`);
+      }
+
+      // Delete enough to trigger merges.
+      for (let i = 0; i < 15; i++) {
+        expect(smallTree.delete(i, `v${i}`)).toBe(true);
+      }
+
+      expect(smallTree.size).toBe(5);
+
+      // Remaining keys should be intact.
+      for (let i = 15; i < 20; i++) {
+        expect(smallTree.get(i)).toEqual(new Set([`v${i}`]));
+      }
+    });
+  });
+
+  // -------------------------------------------------------------------------
+  // String keys
+  // -------------------------------------------------------------------------
+
+  describe('string keys', () => {
+    it('should work with string keys using default comparator', () => {
+      const strTree = new BPlusTree<string, number>();
+      strTree.insert('banana', 1);
+      strTree.insert('apple', 2);
+      strTree.insert('cherry', 3);
+
+      const entries = [...strTree.entries()];
+      expect(entries.map((e) => e.key)).toEqual(['apple', 'banana', 'cherry']);
+      expect(strTree.get('banana')).toEqual(new Set([1]));
+    });
+
+    it('should support string range queries', () => {
+      const strTree = new BPlusTree<string, number>();
+      const words = ['apple', 'banana', 'cherry', 'date', 'elderberry', 'fig'];
+      words.forEach((w, i) => strTree.insert(w, i));
+
+      const result = strTree.range('banana', 'elderberry');
+      expect(result.map((e) => e.key)).toEqual(['banana', 'cherry', 'date']);
+    });
+  });
+});

src/utils/btree.ts

@@ -0,0 +1,553 @@
+/**
+ * Generic comparator function. Returns negative if a < b, positive if a > b, 0 if equal.
+ */
+export type Comparator<K> = (a: K, b: K) => number;
+
+/**
+ * Options for range queries.
+ */
+export type RangeOptions = {
+  /** Whether the lower bound is inclusive (default: true). */
+  lowerInclusive?: boolean;
+  /** Whether the upper bound is inclusive (default: false). */
+  upperInclusive?: boolean;
+};
+
+/**
+ * A single entry returned by range queries and iteration.
+ */
+export type BPlusTreeEntry<K, V> = {
+  key: K;
+  values: Set<V>;
+};
+
+// ---------------------------------------------------------------------------
+// Node types
+// ---------------------------------------------------------------------------
+
+/**
+ * Internal (non-leaf) node. Stores keys that guide searches and pointers
+ * to child nodes. Does NOT store values — all values live in leaves.
+ */
+class InternalNode<K, V> {
+  keys: K[] = [];
+  children: Array<InternalNode<K, V> | LeafNode<K, V>> = [];
+}
+
+/**
+ * Leaf node. Stores key/value-set pairs and maintains a doubly-linked
+ * list across all leaves for efficient range scans.
+ */
+class LeafNode<K, V> {
+  keys: K[] = [];
+  values: Array<Set<V>> = [];
+  next: LeafNode<K, V> | null = null;
+  prev: LeafNode<K, V> | null = null;
+}
+
+type Node<K, V> = InternalNode<K, V> | LeafNode<K, V>;
+
+function isLeaf<K, V>(node: Node<K, V>): node is LeafNode<K, V> {
+  return node instanceof LeafNode;
+}
+
+// ---------------------------------------------------------------------------
+// Default comparator
+// ---------------------------------------------------------------------------
+
+/**
+ * Default comparator using native `<` / `>` operators.
+ * Works correctly for numbers, strings, and Dates.
+ */
+function defaultComparator<K>(a: K, b: K): number {
+  if (a < b) return -1;
+  if (a > b) return 1;
+  return 0;
+}
+
+// ---------------------------------------------------------------------------
+// B+ Tree
+// ---------------------------------------------------------------------------
+
+/**
+ * In-memory B+ Tree with duplicate-key support.
+ *
+ * Each unique key maps to a `Set<V>`, allowing multiple values to share
+ * the same key (e.g. many documents with the same indexed field value).
+ *
+ * Leaf nodes are linked in a doubly-linked list so range scans are O(k)
+ * after the initial O(log n) descent.
+ *
+ * @typeParam K - Key type (must be comparable via the provided comparator)
+ * @typeParam V - Value type stored in each key's Set
+ */
+export class BPlusTree<K, V> {
+  /** Maximum number of keys per node. A node splits when it exceeds this. */
+  private readonly maxKeys: number;
+
+  /** Minimum number of keys a non-root node must hold after deletion. */
+  private readonly minKeys: number;
+
+  private readonly compare: Comparator<K>;
+
+  private root: Node<K, V>;
+
+  /** Total number of individual values across all keys. */
+  private _size = 0;
+
+  constructor(order = 32, comparator?: Comparator<K>) {
+    if (order < 3) throw new Error('B+ Tree order must be at least 3');
+    this.maxKeys = order - 1;
+    this.minKeys = Math.ceil(order / 2) - 1;
+    this.compare = comparator ?? defaultComparator;
+    this.root = new LeafNode<K, V>();
+  }
+
+  // -------------------------------------------------------------------------
+  // Public API
+  // -------------------------------------------------------------------------
+
+  /** Total number of individual values stored in the tree. */
+  get size(): number {
+    return this._size;
+  }
+
+  /** Remove all entries from the tree. */
+  clear(): void {
+    this.root = new LeafNode<K, V>();
+    this._size = 0;
+  }
+
+  /**
+   * Insert a value under the given key. If the key already exists the
+   * value is added to its Set; otherwise a new key entry is created.
+   */
+  insert(key: K, value: V): void {
+    const leaf = this.findLeaf(key);
+    const idx = this.leafKeyIndex(leaf, key);
+
+    if (idx < leaf.keys.length && this.compare(leaf.keys[idx], key) === 0) {
+      // Key exists — add to its value set.
+      const before = leaf.values[idx].size;
+      leaf.values[idx].add(value);
+      this._size += leaf.values[idx].size - before;
+    } else {
+      // New key — splice into position.
+      leaf.keys.splice(idx, 0, key);
+      leaf.values.splice(idx, 0, new Set([value]));
+      this._size++;
+    }
+
+    // Split if the leaf overflows.
+    if (leaf.keys.length > this.maxKeys) {
+      this.splitLeaf(leaf);
+    }
+  }
+
+  /**
+   * Look up all values associated with the exact key.
+   * Returns `undefined` if the key is not present.
+   */
+  get(key: K): Set<V> | undefined {
+    const leaf = this.findLeaf(key);
+    const idx = this.leafKeyIndex(leaf, key);
+    if (idx < leaf.keys.length && this.compare(leaf.keys[idx], key) === 0) {
+      return leaf.values[idx];
+    }
+    return undefined;
+  }
+
+  /**
+   * Delete a value (or all values) for the given key.
+   *
+   * - If `value` is provided, only that value is removed from the key's Set.
+   *   The key entry is removed when its Set becomes empty.
+   * - If `value` is omitted, the entire key entry (with all values) is removed.
+   *
+   * @returns `true` if something was removed, `false` if the key/value wasn't found.
+   */
+  delete(key: K, value?: V): boolean {
+    const leaf = this.findLeaf(key);
+    const idx = this.leafKeyIndex(leaf, key);
+
+    if (idx >= leaf.keys.length || this.compare(leaf.keys[idx], key) !== 0) {
+      return false;
+    }
+
+    if (value !== undefined) {
+      const set = leaf.values[idx];
+      if (!set.has(value)) return false;
+      set.delete(value);
+      this._size--;
+
+      if (set.size > 0) return true;
+      // Set empty — fall through to remove the key entry entirely.
+    } else {
+      this._size -= leaf.values[idx].size;
+    }
+
+    leaf.keys.splice(idx, 1);
+    leaf.values.splice(idx, 1);
+
+    // Rebalance if needed (skip for root leaf).
+    if (leaf !== this.root && leaf.keys.length < this.minKeys) {
+      this.rebalanceLeaf(leaf);
+    }
+
+    // Shrink tree height if the root internal node has a single child.
+    if (!isLeaf(this.root) && this.root.children.length === 1) {
+      this.root = this.root.children[0];
+    }
+
+    return true;
+  }
+
+  /**
+   * Range query. Returns all entries whose keys fall within `[min, max]`
+   * (bounds configurable via `opts`).
+   *
+   * - Omit `min` for an unbounded lower end.
+   * - Omit `max` for an unbounded upper end.
+   * - Omit both to iterate the entire tree in key order.
+   *
+   * Default bounds: lower inclusive, upper exclusive (half-open interval).
+   */
+  range(
+    min?: K,
+    max?: K,
+    opts?: RangeOptions,
+  ): BPlusTreeEntry<K, V>[] {
+    const lowerInc = opts?.lowerInclusive ?? true;
+    const upperInc = opts?.upperInclusive ?? false;
+
+    const results: BPlusTreeEntry<K, V>[] = [];
+
+    // Find the starting leaf.
+    let leaf: LeafNode<K, V>;
+    let startIdx: number;
+
+    if (min !== undefined) {
+      leaf = this.findLeaf(min);
+      startIdx = this.leafKeyIndex(leaf, min);
+      // Adjust for exclusive lower bound.
+      if (!lowerInc && startIdx < leaf.keys.length && this.compare(leaf.keys[startIdx], min) === 0) {
+        startIdx++;
+      }
+    } else {
+      leaf = this.firstLeaf();
+      startIdx = 0;
+    }
+
+    // Walk the leaf chain collecting matching entries.
+    let currentLeaf: LeafNode<K, V> | null = leaf;
+    let i = startIdx;
+
+    while (currentLeaf) {
+      while (i < currentLeaf.keys.length) {
+        const key = currentLeaf.keys[i];
+
+        if (max !== undefined) {
+          const cmp = this.compare(key, max);
+          if (cmp > 0 || (cmp === 0 && !upperInc)) {
+            return results;
+          }
+        }
+
+        results.push({ key, values: currentLeaf.values[i] });
+        i++;
+      }
+
+      currentLeaf = currentLeaf.next;
+      i = 0;
+    }
+
+    return results;
+  }
+
+  /**
+   * Iterate over all entries in key order.
+   */
+  *entries(): IterableIterator<BPlusTreeEntry<K, V>> {
+    let leaf: LeafNode<K, V> | null = this.firstLeaf();
+    while (leaf) {
+      for (let i = 0; i < leaf.keys.length; i++) {
+        yield { key: leaf.keys[i], values: leaf.values[i] };
+      }
+      leaf = leaf.next;
+    }
+  }
+
+  // -------------------------------------------------------------------------
+  // Tree navigation
+  // -------------------------------------------------------------------------
+
+  /**
+   * Descend to the leaf node that should contain the given key.
+   */
+  private findLeaf(key: K): LeafNode<K, V> {
+    let node: Node<K, V> = this.root;
+    while (!isLeaf(node)) {
+      const internal = node as InternalNode<K, V>;
+      let childIdx = internal.keys.length;
+      for (let i = 0; i < internal.keys.length; i++) {
+        if (this.compare(key, internal.keys[i]) < 0) {
+          childIdx = i;
+          break;
+        }
+      }
+      node = internal.children[childIdx];
+    }
+    return node;
+  }
+
+  /** Get the leftmost leaf in the tree. */
+  private firstLeaf(): LeafNode<K, V> {
+    let node: Node<K, V> = this.root;
+    while (!isLeaf(node)) {
+      node = (node as InternalNode<K, V>).children[0];
+    }
+    return node;
+  }
+
+  /**
+   * Binary search within a leaf for the insertion position of `key`.
+   * Returns the index of the first key >= `key`.
+   */
+  private leafKeyIndex(leaf: LeafNode<K, V>, key: K): number {
+    let lo = 0;
+    let hi = leaf.keys.length;
+    while (lo < hi) {
+      const mid = (lo + hi) >>> 1;
+      if (this.compare(leaf.keys[mid], key) < 0) {
+        lo = mid + 1;
+      } else {
+        hi = mid;
+      }
+    }
+    return lo;
+  }
+
+  // -------------------------------------------------------------------------
+  // Splitting
+  // -------------------------------------------------------------------------
+
+  /**
+   * Split an overflowing leaf node. The right half becomes a new leaf,
+   * and a copy of its first key is promoted to the parent.
+   */
+  private splitLeaf(leaf: LeafNode<K, V>): void {
+    const mid = Math.ceil(leaf.keys.length / 2);
+    const newLeaf = new LeafNode<K, V>();
+
+    newLeaf.keys = leaf.keys.splice(mid);
+    newLeaf.values = leaf.values.splice(mid);
+
+    // Maintain the doubly-linked list.
+    newLeaf.next = leaf.next;
+    newLeaf.prev = leaf;
+    if (leaf.next) leaf.next.prev = newLeaf;
+    leaf.next = newLeaf;
+
+    const promotedKey = newLeaf.keys[0];
+    this.insertIntoParent(leaf, promotedKey, newLeaf);
+  }
+
+  /**
+   * Split an overflowing internal node. The middle key is pushed up
+   * to the parent (not copied — it's removed from this level).
+   */
+  private splitInternal(node: InternalNode<K, V>): void {
+    const mid = Math.floor(node.keys.length / 2);
+    const promotedKey = node.keys[mid];
+
+    const newNode = new InternalNode<K, V>();
+    newNode.keys = node.keys.splice(mid + 1);
+    newNode.children = node.children.splice(mid + 1);
+    node.keys.splice(mid, 1); // remove the promoted key
+
+    this.insertIntoParent(node, promotedKey, newNode);
+  }
+
+  /**
+   * Insert a promoted key and new right child into the parent of `left`.
+   * If `left` is the root, a new root is created.
+   */
+  private insertIntoParent(
+    left: Node<K, V>,
+    key: K,
+    right: Node<K, V>,
+  ): void {
+    if (left === this.root) {
+      const newRoot = new InternalNode<K, V>();
+      newRoot.keys = [key];
+      newRoot.children = [left, right];
+      this.root = newRoot;
+      return;
+    }
+
+    const parent = this.findParent(this.root, left) as InternalNode<K, V>;
+    const idx = parent.children.indexOf(left);
+
+    parent.keys.splice(idx, 0, key);
+    parent.children.splice(idx + 1, 0, right);
+
+    if (parent.keys.length > this.maxKeys) {
+      this.splitInternal(parent);
+    }
+  }
+
+  // -------------------------------------------------------------------------
+  // Rebalancing (deletion)
+  // -------------------------------------------------------------------------
+
+  /**
+   * Rebalance a leaf that has fewer than `minKeys` entries after deletion.
+   * Tries to borrow from a sibling first; if neither sibling can spare
+   * a key, merges with a sibling.
+   */
+  private rebalanceLeaf(leaf: LeafNode<K, V>): void {
+    const parent = this.findParent(this.root, leaf) as InternalNode<K, V>;
+    const idx = parent.children.indexOf(leaf);
+
+    // Try borrowing from the right sibling.
+    if (idx < parent.children.length - 1) {
+      const rightSibling = parent.children[idx + 1] as LeafNode<K, V>;
+      if (rightSibling.keys.length > this.minKeys) {
+        leaf.keys.push(rightSibling.keys.shift()!);
+        leaf.values.push(rightSibling.values.shift()!);
+        parent.keys[idx] = rightSibling.keys[0];
+        return;
+      }
+    }
+
+    // Try borrowing from the left sibling.
+    if (idx > 0) {
+      const leftSibling = parent.children[idx - 1] as LeafNode<K, V>;
+      if (leftSibling.keys.length > this.minKeys) {
+        leaf.keys.unshift(leftSibling.keys.pop()!);
+        leaf.values.unshift(leftSibling.values.pop()!);
+        parent.keys[idx - 1] = leaf.keys[0];
+        return;
+      }
+    }
+
+    // Merge with a sibling.
+    if (idx < parent.children.length - 1) {
+      this.mergeLeaves(leaf, parent.children[idx + 1] as LeafNode<K, V>, parent, idx);
+    } else {
+      this.mergeLeaves(parent.children[idx - 1] as LeafNode<K, V>, leaf, parent, idx - 1);
+    }
+  }
+
+  /**
+   * Merge `right` leaf into `left` leaf and remove the separator key
+   * from the parent.
+   */
+  private mergeLeaves(
+    left: LeafNode<K, V>,
+    right: LeafNode<K, V>,
+    parent: InternalNode<K, V>,
+    separatorIdx: number,
+  ): void {
+    left.keys.push(...right.keys);
+    left.values.push(...right.values);
+
+    // Fix linked list pointers.
+    left.next = right.next;
+    if (right.next) right.next.prev = left;
+
+    // Remove the separator key and right child from the parent.
+    parent.keys.splice(separatorIdx, 1);
+    parent.children.splice(separatorIdx + 1, 1);
+
+    // Recursively rebalance the parent if needed.
+    if (parent !== this.root && parent.keys.length < this.minKeys) {
+      this.rebalanceInternal(parent);
+    }
+  }
+
+  /**
+   * Rebalance an internal node that has too few keys after a merge.
+   */
+  private rebalanceInternal(node: InternalNode<K, V>): void {
+    const parent = this.findParent(this.root, node) as InternalNode<K, V>;
+    const idx = parent.children.indexOf(node);
+
+    // Try borrowing from the right sibling.
+    if (idx < parent.children.length - 1) {
+      const rightSibling = parent.children[idx + 1] as InternalNode<K, V>;
+      if (rightSibling.keys.length > this.minKeys) {
+        node.keys.push(parent.keys[idx]);
+        parent.keys[idx] = rightSibling.keys.shift()!;
+        node.children.push(rightSibling.children.shift()!);
+        return;
+      }
+    }
+
+    // Try borrowing from the left sibling.
+    if (idx > 0) {
+      const leftSibling = parent.children[idx - 1] as InternalNode<K, V>;
+      if (leftSibling.keys.length > this.minKeys) {
+        node.keys.unshift(parent.keys[idx - 1]);
+        parent.keys[idx - 1] = leftSibling.keys.pop()!;
+        node.children.unshift(leftSibling.children.pop()!);
+        return;
+      }
+    }
+
+    // Merge with a sibling.
+    if (idx < parent.children.length - 1) {
+      const rightSibling = parent.children[idx + 1] as InternalNode<K, V>;
+      this.mergeInternal(node, rightSibling, parent, idx);
+    } else {
+      const leftSibling = parent.children[idx - 1] as InternalNode<K, V>;
+      this.mergeInternal(leftSibling, node, parent, idx - 1);
+    }
+  }
+
+  /**
+   * Merge two internal nodes by pulling down the separator key from the
+   * parent and concatenating children.
+   */
+  private mergeInternal(
+    left: InternalNode<K, V>,
+    right: InternalNode<K, V>,
+    parent: InternalNode<K, V>,
+    separatorIdx: number,
+  ): void {
+    left.keys.push(parent.keys[separatorIdx]);
+    left.keys.push(...right.keys);
+    left.children.push(...right.children);
+
+    parent.keys.splice(separatorIdx, 1);
+    parent.children.splice(separatorIdx + 1, 1);
+
+    if (parent !== this.root && parent.keys.length < this.minKeys) {
+      this.rebalanceInternal(parent);
+    }
+  }
+
+  // -------------------------------------------------------------------------
+  // Utilities
+  // -------------------------------------------------------------------------
+
+  /**
+   * Walk the tree from `current` downward to find the parent of `target`.
+   * Returns `null` if `target` is the root or not found.
+   */
+  private findParent(
+    current: Node<K, V>,
+    target: Node<K, V>,
+  ): InternalNode<K, V> | null {
+    if (isLeaf(current)) return null;
+    const internal = current as InternalNode<K, V>;
+
+    for (const child of internal.children) {
+      if (child === target) return internal;
+      const found = this.findParent(child, target);
+      if (found) return found;
+    }
+
+    return null;
+  }
+}

src/utils/index.ts

@@ -1,3 +1,4 @@
 export * from './event-emitter.js';
 export * from './exponential-backoff.js';
 export * from './sse-session.js';
+export * from './btree.js';