- Bloom filter:
- Bloom filter =
a space-efficient
probabilistic data structure
used to test
whether an element
is a member of a
set.
- Probabilistic nature of a
bloom filter:
- False positive matches
in a bloom filter
are possible
- False negative matches in a bloom filter are impossible
- False positive matches
in a bloom filter
are possible
- Bloom filter =
a space-efficient
probabilistic data structure
used to test
whether an element
is a member of a
set.
- A Bloom filter consists of:
- A bit array of
m bits
(initially, all bits are
reset to 0)
- k different hash functions
- A bit array of
m bits
(initially, all bits are
reset to 0)
- Creating the
Bloom filter for
a set of
elements:
/* ====================================== Initialize Blook filter ====================================== */ for ( i = 0; i < m; i++ ) BloomFilterBit[i] = 0; /* ========================================== Creating the Bloom filter for n elements ========================================== */ for ( each element x in set ) do { for ( j = 0; j < k; j++ ) { rand = hashj( x ); BloomFilterBit[rand] = 1; } }
- Using
a Bloom filter:
- The check if
an element
u is an
element of the
set:
isElement = true; for ( j = 0; j < k; j++ ) { rand = hashj( u ); if ( BloomFilterBit[rand] == 0 ) { isElement = false; // Hash miss - cann't be element of set ! } }
Notice that:
- There are no
false negatives:
- If one of the hash values does not match, the element can not be in the original set !!!
So we will identify all elements of the original set (and maybe more)
- There are possibly
false positives:
- A bogus element can produce hash values that are set in the Bloom filter array
So we may get more elements than those in the original set....
- The check if
an element
u is an
element of the
set:
- Nice webpage to experiment with
Bloom filters:
click here
- How to
eliminate
most
dangling tuples
using a Bloom filter:
- Compute the
Bloom filter of
πY(S) and
transfer the
Bloom bit array to
R's site:
- Use the Bloom filter to
extract
the candidate set and
transfer the
result to
S's site:
- Perform
subset(R) ⋈ S
at
S's site:
- Compute the
Bloom filter of
πY(S) and
transfer the
Bloom bit array to
R's site: