Quiz 2

Frequency Estimation in Streams

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Python Week 1: the first filter for runtime behavior
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# Frequency Estimation in Streams ## Count-Min Sketch vs Count Sketch Property Count-Min Count Estimate bias Overestimates (never underestimates) Unbiased Space $O(\frac{1}{\epsilon} \log \frac{1}{\delta})$ $O(\frac{1}{\epsilon^2} \log \frac{1}{\delta})$ Update time $O(\log \frac{1}{\delta})$ $O(\log \frac{1}{\delta...

Frequency Estimation in Streams

Count-Min Sketch vs Count Sketch

PropertyCount-MinCount
Estimate biasOverestimates (never underestimates)Unbiased
SpaceO(1ϵlog1δ)O(\frac{1}{\epsilon} \log \frac{1}{\delta})O(1ϵ2log1δ)O(\frac{1}{\epsilon^2} \log \frac{1}{\delta})
Update timeO(log1δ)O(\log \frac{1}{\delta})O(log1δ)O(\log \frac{1}{\delta})
Error guarantee$

Count-Min Sketch: Guarantee

For any query ii, with probability 1δ1 - \delta:
f^ifi+ϵf1\hat{f}_i \leq f_i + \epsilon ||f||_1
Where f1||f||_1 is the sum of all frequencies, ϵ\epsilon is error parameter, δ\delta is failure probability. Join Discord PreviousMatrix SketchingNextStreaming Algorithms
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