1. A Memory-optimized Bloom Filter using An Additional Hashing Function Author: Mahmood Ahmadi, Stephan Wong Publisher: IEEE GLOBECOM 2008 Presenter: Yu-Ping Chiang Date: 2009/04/29

2. Outline Related work  Regular bloom filter  Pruned bloom filter BFAH (bloom filter with an additional hashing function) Performance

3. Regular bloom filter Address 0 2 1 6 3 5 4 8 7 10 9 11 Bit-array 1 1 0 1 0 1 1 1 0 1 0 0 R0 R2 R3 R1 H1(R1) H2(R1) H3(R1) R0 R1 R0 R1 R2 R3 R2 R3 R0

4. Regular bloom filter - search Address 0 2 1 6 3 5 4 8 7 10 9 11 Bit-array 1 1 0 1 0 1 1 1 0 1 0 0 Input: X H1(X) H3(X) R0 R1 R0 R1 R2 R3 R2 R3 H2(X) R0 NO match any rule !! Disadvantages: ‧ Can’t delete rule ‧ Duplicate rules in memory

5. Pruned bloom filter Bit-array 1 1 0 1 0 1 1 1 0 1 0 0 Address 0 2 1 6 3 5 4 8 7 10 9 11 R0 R2 R3 R1 R0 R1 R2 R3 2 3 0 1 0 2 1 2 0 1 0 0 Counter ‧ After set bit-array for all rules, save rule only in smallest counter position.

6. Outline Related work  Regular bloom filter  Pruned bloom filter BFAH (bloom filter with an additional hashing function) Performance

7. BFAH Determine which place will use to insert item. Address 0 2 1 6 3 5 4 8 7 10 9 11 Bit-array 1 1 0 1 0 1 1 1 0 1 0 0 R0 R2 R3 R1 H1(R1) H2(R1) H3(R1) Additional hash function

8. BFAH - example Address 0 2 1 6 3 5 4 8 7 10 9 11 Bit-array 1 1 0 0 0 0 1 0 0 0 0 0 R0 H1(R1) H2(R1) H3(R1) Additional hash function rule_num mod 3 Input : 0 Output : 0 R0

9. BFAH - example Address 0 2 1 6 3 5 4 8 7 10 9 11 Bit-array 1 1 0 0 0 1 1 0 0 0 0 0 R0 R1 Additional hash function rule_num mod 3 Input : 1 Output : 1 R0 R1

10. BFAH - example Address 0 2 1 6 3 5 4 8 7 10 9 11 Bit-array 1 1 0 1 0 1 1 1 0 1 0 0 R0 R2 R3 R1 Additional hash function rule_num mod 3 R0 R1 R3 R2

11. Outline Related work  Regular bloom filter  Pruned bloom filter BFAH (bloom filter with an additional hashing function) Performance

12. R.B : Regular Bloom filter P.C.B : Pruned Counting Bloom filter M.B : BFAH k = # of hash functions m = size of bit array n = # of items (rules)

13. Performance R.B : Regular Bloom filter P.C.B : Pruned Counting Bloom filter M.B : BFAH k = # of hash functions m = size of bit array n = # of items (rules)

14. Performance Average number of collisions for all rule-set.