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Unformatted text preview: 1 More StreamMining Counting How Many Elements Computing Moments 2 Counting Distinct Elements r Problem : a data stream consists of elements chosen from a set of size n . Maintain a count of the number of distinct elements seen so far. r Obvious approach : maintain the set of elements seen. 3 Applications r How many different words are found among the Web pages being crawled at a site? R Unusually low or high numbers could indicate artificial pages (spam?). r How many different Web pages does each customer request in a week? 4 Using Small Storage r Real Problem : what if we do not have space to store the complete set? r Estimate the count in an unbiased way. r Accept that the count may be in error, but limit the probability that the error is large. 5 FlajoletMartin* Approach r Pick a hash function h that maps each of the n elements to log 2 n bits, uniformly. R Important that the hash function be (almost) a random permutation of the elements. r For each stream element a , let r ( a ) be the number of trailing 0s in h ( a )....
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 Fall '09

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