Parallel and Distributed Programming

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Parallel and Distributed Programming

• Tran Vinh Cuong
• Department of Computer Science

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Bloom filter

• Conceived by Burton H. Bloom in 1970, is a
  space-efficient probabilistic data structure that
  is used to test whether an element is a member of
  a set.
• False positives are possible, but false negatives
  are not.
• Elements can be added to the set, but not
  removed.
• The more elements are added to the set, the
  larger the probability of false positives.

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Bloom filter algorithm

• An empty bloom filter is a bit array of m bits,
  all set to 0.
• There are k different hash functions.
• Add element feed it to k hash functions, and get
  k different array positions. Set these positions
  to 1.
• Check existence feed it to k hash functions, get
  k array positions. If any of these positions is 0
  -gt not in the set.

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Probability of false positive
Assume hash functions select each array position
with equal probability. The probability of a
certain bit is not set to 1 by a hash function
during insertion of an element is
The probability of that bit is not set by any of
k hash functions is
After inserting r elements, the probability that
it is still 0 is
The probability that it is 1 is therefore
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Test existence of an element that is not in the
set
The probability of all of k positions being 1,
(false positive)
This is the upper bound probability of hash
collision on the first r elements (states)
entered. And it is minimal when
m 109, r107 P(hash collision)
10-21 k89.315
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Trade-off

• In SPIN k 2, prob. 4.10-4, average coverage
  search reduces from 100 to 99