A probabilistic data structure used to estimate the frequency of events in a data stream with low memory requirements.
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📈 🔢 ⏳
Story
The Count-Min Sketch is a probabilistic data structure that efficiently estimates the frequency of elements (events) in a data stream using minimal memory. It was introduced by Cormode and Muthukrishnan in 2003.
TakeAways
- 📌 The Count-Min Sketch is a space-efficient algorithm used for estimating the frequency of events in large data streams, offering a trade-off between memory usage and estimation accuracy.
- 💡 It uses multiple hash functions to map elements to buckets within an array, with each bucket having a count that represents the estimated frequency of the mapped element.
- 🔍 The structure has two parameters: width (
w) and depth (d), determining its memory size and estimation error rate.
Process
- Initialization: Create a 2D array with w columns and d rows, initialized to zero.
- Hash Functions: Apply d independent hash functions on each incoming element e to determine its position within the array using indices (h₁(e), h₂(e), …, hᵢ(e)).
- Count Update: Increment the value at the determined position for each hash function: A[h₁(e)][0], A[h₁(e)][1], …, A[hᵢ(e)][d-1].
- Frequency Estimation: The estimated frequency of element e is the minimum value among all positions: min(A[h₁(e)][0], A[h₁(e)][1], …, A[hᵢ(e)][d-1]).
- Error Analysis: The probability of overestimation is 1/w, while underestimation has a more complex analysis based on the number of collisions between elements.
Thoughts
- 📈 Accuracy vs. Memory Trade-off: By adjusting width (
w) and depth (d), one can balance memory usage against estimation accuracy. - 🔢 Collision Handling: The Count-Min Sketch handles collisions probabilistically, reducing the need for complex data structures or excessive memory allocation.
- ⏳ Real-time Applications: This structure is suitable for real-time data analysis and monitoring applications where low latency and high throughput are essential.