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On Adding Bloom Filters to Longest
Prefix Matching Algorithms
Author: Hyesook Lim, Kyuhee Lim, Nara Lee, and Kyong-hye Park
Publisher: IEEE TRANSACTIONS ON COMPUTERS
Presenter: Yuen-Shuo Li
Date: 2012/09/17
Outline
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Idea
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Bloom Filter
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Parallel Multiple-Hashing
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Binary Search on Trie Levels
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Performance
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Conclusion
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Idea
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Bloom Filter(1/4)
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used to test whether an element is a member of a set
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have a strong space and time advantage
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Elements can be added to the set, but not removed
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FAST!
Bloom Filter(2/4)
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False positives retrieval results are possible.
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But false negatives are not.
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positive may be wrong!
Bloom Filter(3/4)
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a bit-vector
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multiple hash function
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Bloom Filter(4/4)
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It is important to properly control the rate of the false positive in designing a
Bloom filter.
𝑘=
𝑚
2 log2 𝑛
ln 2
k: hash functions
m: array size
n: element size
Parallel Multiple-Hashing(1/3)
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parallel hashing for each prefix length
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use multiple-hash functions to reduce
collisions
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Parallel Multiple-Hashing(2/3)
Adding a Bloom Filter
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to reduce the implementation complexity
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Parallel Multiple-Hashing(3/3)
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reduce the implementation complexity
parallel is not necessary since filter filters out the length of the input
Binary Search on Trie Levels(1/4)
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separates the binary trie, according to the level of the trie
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markers are pre-computed in the internal nodes
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Binary Search on Trie Levels(2/4)
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for a 6-bit input 111000
P5
done!
not match
Binary Search on Trie Levels(3/4)
Bloom filter
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filters out each input that does not have a node in the binary trie
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Binary Search on Trie Levels(4/4)
Leaf-Pushed Trie
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uses leaf-pushing to make every prefix disjoint
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finishes a search when a match to a prefix occurs
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Performance
search performance with and without Bloom filter for PMH
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Performance
search performance with and without Bloom filter for W-BSL
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Performance
search performance with and without Bloom filter for L-BSL
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Conclusion
Bloom filter is a simple but extremely powerful data structure that will
improve the performance.
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Thanks