Lecture10

Lecture10 - Lecture 10, Oct 21 2010 Bloom Filter Analysis...

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1 115 Bloom Filter Analysis After all elements are hashed, probability of specific bit in A still being zero: Probability of false positive is What is the “right” number of hash functions ( k ) ? » Two competing factors: Larger k increases probability of finding zero if the element is not in the set (good) Too large k will fill A with too many ones (p too small - bad) (1 p ) k p = ¡ 1 1 m ¢ kn = ¡¡ 1 1 m ¢ m ¢ kn m e kn m using (1 1 m ) m e 1 Lecture 10, Oct 21 2010 116 Analysis continued Rewrite false positive probability: We will try to minimize the argument of the exponent. Using rewrite the exponent as a function of p: From symmetry considerations, the minimum is at p=0.5: For this value of k, the false positive rate is k ln(1 e kn/m )= m n ln p ln(1 p ) p e kn/m (0 . 5) k =(0 . 62) m/n (1 p ) k ¡ 1 e kn/m ¢ k =exp( k ln(1 e kn/m )) k = m n ln 2
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2 Example Consider m/n=10 If k=1, then false positive probability is
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This note was uploaded on 03/08/2011 for the course CS 161 at Stanford.

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Lecture10 - Lecture 10, Oct 21 2010 Bloom Filter Analysis...

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