Probabilistic Programming and Data Structures

  1. Membership and Set Operations
    1. Bloom Filters
      1. Basic Structure and Operations
        1. Bit Array Representation
          1. Multiple Hash Functions
            1. Insertion Algorithm
              1. Query Algorithm
              2. Error Analysis
                1. False Positive Probability
                  1. Optimal Parameter Selection
                    1. No False Negatives Guarantee
                    2. Parameter Optimization
                      1. Bit Array Size Selection
                        1. Number of Hash Functions
                          1. Memory-Error Tradeoffs
                          2. Variants and Extensions
                            1. Counting Bloom Filters
                              1. Counter Arrays
                                1. Deletion Support
                                  1. Counter Overflow Handling
                                  2. Scalable Bloom Filters
                                    1. Dynamic Growth
                                      1. Multiple Filter Levels
                                      2. Compressed Bloom Filters
                                        1. Space Optimization
                                          1. Compression Techniques
                                          2. Spectral Bloom Filters
                                            1. Frequency Information
                                              1. Multi-Set Support
                                          3. Cuckoo Filters
                                            1. Cuckoo Hashing Principles
                                              1. Two Hash Functions
                                                1. Displacement Strategy
                                                  1. Load Factor Limits
                                                  2. Filter Construction
                                                    1. Fingerprint Generation
                                                      1. Bucket Organization
                                                        1. Insertion Algorithm
                                                        2. Query and Deletion
                                                          1. Membership Testing
                                                            1. Item Removal
                                                              1. False Positive Analysis
                                                              2. Comparison with Bloom Filters
                                                                1. Space Efficiency
                                                                  1. Deletion Capability
                                                                    1. Performance Characteristics

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                                                                6. Probabilistic Data Structures Theory

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                                                                8. Cardinality Estimation