Implementing Efficient Prefix Search with Tries

• Membership: "Does any string start with cap?"

• Enumeration: "List (or count) all strings with prefix cap."

• Analytics: "How many keys share prefix user/123/?" "Give me the next 100 after cap in lexicographic order."

Core Algorithm: The Trie (Prefix Tree)

Building the Trie

1. Insert all terms and raw frequencies.

2. Post-process with a single DFS: each node merges children’s top-K into its own, keeping only K.

3. Optionally compress single-child chains (“path compression” / radix tree) to reduce memory and cache misses.

Core Operations

• insert(s): Walk/allocate nodes along s, mark terminal.

• contains(s): Walk; check terminal flag.

• has_prefix(p): Walk; success if the node exists.

• count(p): Requires maintaining a subtree_size counter at each node (incremented/decremented on insert/delete).

• enumerate(p, K): Walk to node of p, then DFS/BFS until K terminals.

Prefix Search at Scale

Caching Top Suggestions at Every Node

1. The Cache
At every node N, maintain a small fixed list (e.g., Top 10) of the most popular or relevant search terms within N’s sub-tree.

2. Lookup Efficiency
A query for prefix P traverses only O(|p|) steps to locate the prefix node, then instantly reads its cached list.
• Total query time: O(|p| + K)
• Independent of total vocabulary size.

3. Memory Optimization
Storing full strings redundantly at each node wastes space. Instead, cache:
• A reference or pointer to the terminal node of each suggested term.
• The ranking score or frequency.
Reconstructing the suggestion (e.g., "captain") involves walking parent pointers back to the root to rebuild the string.
This approach dramatically reduces storage overhead while keeping the hot paths fast.

Maintaining the Cache: Incremental Updates

1. Terminal Update
When a term’s frequency changes (e.g., after a search event or batch re-aggregation), update its score at the terminal node.

2. Upward Recalculation
Walk upward toward the root:
• If the term already exists in a parent’s Top K, update its score in place.
• If it’s new and outranks the parent’s lowest entry, insert it and evict the weakest.
• Otherwise, stop — since all higher ancestors will already have stronger candidates.

Persistence and Cold-Start Readiness

• Snapshotting:
Periodically serialize the trie in preorder traversal to disk.
Each node must record its:
• Edge label (for compressed/radix variants)
• Terminal flag
• Top K cache entries
• Child count or offsets for deserialization.

• Memory-Mapped Loading:
For large vocabularies (millions of nodes), store the serialized trie in a flat binary format designed for memory-mapping (mmap).
On startup, the process maps the file directly into virtual memory — no parsing or rebuilding required.
Queries can execute immediately, delivering instant cold-start readiness.

Tips

• Choosing K: Usually 5–20 is enough. Larger caches grow memory superlinearly.

• Weighted Scores: Combine query frequency, click-through, and recency for better relevance.

• Batch Refresh: Rebuild the Top K lists offline hourly or daily; propagate deltas asynchronously.

• Compression: Use Radix edges (multi-character labels) to shrink memory and improve locality.

• Monitoring: Log per-prefix hit ratios and latency to tune caching depth and K-size.

Final thought