{
    "api": "YAML JSON TOON Database",
    "version": "1.0.0",
    "format": "json",
    "dataset": {
        "id": 44,
        "slug": "bloom-filters-probabilistic",
        "title": "Probabilistic Data Structures: Bloom Filters & Beyond",
        "description": "Probabilistic data structures for approximate set membership, counting, and cardinality estimation: Bloom filters, Count-Min Sketch, HyperLogLog, and Cuckoo filters.",
        "category": "Data Structures",
        "category_slug": "data-structures",
        "tags": "bloom-filter,probabilistic,data-structures,hyperloglog,cuckoo-filter,count-min-sketch",
        "view_count": 0,
        "created_at": 1777673262,
        "updated_at": 1777673262
    },
    "data": {
        "structures": [
            {
                "name": "Bloom Filter",
                "type": "Membership",
                "space_usage": "m bits for m-bit array",
                "false_positive_rate": "~ (1 - e^{-kn/m})^k where k = hash count, n = elements, m = bits",
                "operations": ["add", "possibly_contains"],
                "strengths": ["No false negatives", "Constant-time add/query", "Very memory efficient", "No deletion needed for many use cases"],
                "weaknesses": ["Cannot remove elements (counting BF solves this)", "False positives possible", "No way to list stored elements"],
                "use_cases": ["Cache busting (avoid cache misses for non-existent keys)", "Web crawler URL deduplication", "Spam email filtering", "Database query optimization (bloom filter indexes)"],
                "notes": "Optimal hash count k = (m/n) * ln(2). A 10-bit-per-element filter has ~1% false positive rate."
            },
            {
                "name": "Counting Bloom Filter",
                "type": "Membership with Deletion",
                "space_usage": "m × d bits (d = counter width, typically 4 bits)",
                "false_positive_rate": "Same as standard Bloom Filter",
                "operations": ["add", "remove", "possibly_contains"],
                "strengths": ["Supports deletion", "All base Bloom Filter advantages"],
                "weaknesses": ["4-5x more memory than standard Bloom", "Counter overflow risk with small counters"],
                "use_cases": ["Streaming data with deletions", "Cache with TTL-based eviction", "Dynamic sets where removals needed"],
                "notes": "Use 4-bit counters (max 15 increments) to balance memory and overflow risk. Larger d for high-frequency items."
            },
            {
                "name": "Cuckoo Filter",
                "type": "Membership",
                "space_usage": "~ 1.17 bytes per element (for 3% FPR, β = 95% load)",
                "false_positive_rate": "Configurable (typically 1-5%)",
                "operations": ["add", "remove", "contains"],
                "strengths": ["Supports deletion natively", "Better space efficiency than Bloom for low FPR", "Higher load factor (~95%)"],
                "weaknesses": ["Insertion may fail (relocation limit)", "More complex implementation", "Relocation chains on insertion"],
                "use_cases": ["Database query acceleration", "Network packet deduplication", "Distributed systems membership"],
                "notes": "Uses cuckoo hashing with two hash functions. When bucket full, existing item is kicked to alternate location."
            },
            {
                "name": "HyperLogLog",
                "type": "Cardinality Estimation",
                "space_usage": "~ 1.5 KB for 2^14 registers (standard), error ~ 1.04/√m",
                "relative_error": "~ 1.04/√m (e.g., 1.5KB → ~2% error for billions)",
                "operations": ["add", "count", "merge"],
                "strengths": ["Extremely memory efficient", "Supports union/merge of independent HLLs", "Well-understood error bounds"],
                "weaknesses": ["Cannot estimate set intersections directly", "Inaccurate for very small cardinalities (bias correction needed)", "Single-set cardinality only"],
                "use_cases": ["Unique visitor counting", "Distinct IP addresses in network traffic", "Reach and frequency estimation", "Big data analytics"],
                "notes": "Presto, Redshift, BigQuery, and Redis all implement HyperLogLog natively. Practical limit: trillions of distinct values."
            },
            {
                "name": "Count-Min Sketch",
                "type": "Frequency Estimation",
                "space_usage": "d × w counters (d = depth, w = width). Typically d=5, w = 2/ε",
                "relative_error": "Overestimates frequency with probability δ for error bound ε",
                "operations": ["add", "estimate_count"],
                "strengths": ["Very space efficient for frequency estimation", "Handles heavy hitters (frequent items) well", "Mergeable across distributed nodes"],
                "weaknesses": ["Always overestimates (never underestimates)", "Cannot remove elements", "Point queries less accurate for low-frequency items"],
                "use_cases": ["Heavy hitters detection (network traffic)", "Frequency estimation in streaming data", "Trending topics/items", "Query optimization in databases"],
                "notes": "Used by Apache DataSketches, Redis (top-k), and network monitoring tools. Set d = ceil(ln(1/δ)), w = ceil(2/ε)."
            },
            {
                "name": "MinHash",
                "type": "Similarity Estimation",
                "space_usage": "k × 64 bits (k = number of hash functions, typically 128-256)",
                "relative_error": "~ 1/√k for Jaccard similarity (e.g., k=256 → ~6% error)",
                "operations": ["add_document", "estimate_similarity", "find_near_duplicates"],
                "strengths": ["Fast similarity estimation for large document sets", "Locality-sensitive hashing variant (LSH)", "Supports union/intersection estimation"],
                "weaknesses": ["Only estimates Jaccard similarity", "Requires many hash functions for accuracy", "Not suitable for exact matching"],
                "use_cases": ["Near-duplicate document detection", "Recommendation systems (similar users/items)", "Large-scale clustering", "Plagiarism detection"],
                "notes": "Foundation for many LSH (Locality-Sensitive Hashing) schemes. Google, Amazon, and Netflix use variants for dedup and recommendations."
            }
        ]
    }
}