Streaming Algorithms

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# Streaming Algorithms ## 9.1 Reservoir Sampling Sample $k$ elements uniformly from a stream of unknown length: ## 9.2 Count-Distinct (HyperLogLog) Estimate the number of distinct elements using $O(\log \log n)$ space. **Idea:** Hash each element, track the longest run of leading zeros.

Streaming Algorithms

9.1 Reservoir Sampling

Sample

k

elements uniformly from a stream of unknown length:


python
import numpy as np
def reservoir_sample(stream, k):
    reservoir = []
    for i, item in enumerate(stream):
        if i < k:
            reservoir.append(item)
        else:
            j = np.random.randint(0, i+1)
            if j < k:
                reservoir[j] = item
    return reservoir

9.2 Count-Distinct (HyperLogLog)

Estimate the number of distinct elements using

O(\log \log n)

space. Idea: Hash each element, track the longest run of leading zeros. If the max run is

R

, estimate

n \approx 2^R

9.3 Heavy Hitters (Misra-Gries)

Find all elements that occur more than

n/k

times using

O(k)

space. Algorithm: Maintain

k-1

counters. For each element, increment if tracked, else decrement all. Elements with positive counters at end are heavy hitter candidates. Join Discord PreviousFrequency EstimationNextHyperLogLog

What this note is really saying

Streaming Algorithms

9.1 Reservoir Sampling

9.2 Count-Distinct (HyperLogLog)

9.3 Heavy Hitters (Misra-Gries)

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