1. 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

2. Outline Idea Bloom Filter Parallel Multiple-Hashing
Binary Search on Trie Levels
Performance
Conclusion

3. Idea

4. Bloom Filter(1/4)
used to test whether an element is a member of a set
have a strong space and time advantage
Elements can be added to the set, but not removed
FAST!

5. Bloom Filter(2/4) positive may be wrong!
False positives retrieval results are possible.
But false negatives are not.
positive may be wrong!

6. Bloom Filter(3/4)
a bit-vector
multiple hash function

7. Bloom Filter(4/4) 𝑘= 𝑚 2 log 2 𝑛 ln 2 k: hash functions m: array size
It is important to properly control the rate of the false positive in designing a Bloom filter.
k: hash functions
m: array size
n: element size
𝑘= 𝑚 log 2 𝑛 ln 2

8. Parallel Multiple-Hashing(1/3)
parallel hashing for each prefix length
use multiple-hash functions to reduce collisions

9. Parallel Multiple-Hashing(2/3)
Adding a Bloom Filter
to reduce the implementation complexity

10. Parallel Multiple-Hashing(3/3)
reduce the implementation complexity
parallel is not necessary since filter filters out the length of the input

11. Binary Search on Trie Levels(1/4)
separates the binary trie, according to the level of the trie
markers are pre-computed in the internal nodes

12. Binary Search on Trie Levels(2/4)
for a 6-bit input P5
done!
not match

13. Binary Search on Trie Levels(3/4)
Bloom filter
filters out each input that does not have a node in the binary trie

14. Binary Search on Trie Levels(4/4)
Leaf-Pushed Trie
uses leaf-pushing to make every prefix disjoint
finishes a search when a match to a prefix occurs

15. Performance
search performance with and without Bloom filter for PMH

16. Performance
search performance with and without Bloom filter for W-BSL

17. Performance
search performance with and without Bloom filter for L-BSL

18. Conclusion
Bloom filter is a simple but extremely powerful data structure that will improve the performance.

19. Thanks