1. 1 Blooming Trees for Minimal Perfect Hashing Author: Gianni Antichi, Domenico Ficara, Stefano Giordano, Gregorio Procissi, Fabio Vitucci Publisher: GLOBECOM 2008 Presenter: Yu-Ping Chiang Date: 2009/07/21

2. 2 Outline Related work  Huffman spectral bloom filter  Blooming tree Minimal Perfect Hash Function  Using naïve blooming tree  Using optimized blooming tree and HSBF Experimental result

3. 3 Related work – Huffman Spectral Bloom Filter Using Huffman code encode Counting Bloom Filter (CBF)  Encode value δ with (δ+1) bits 30010010 0111010000 0 CBF HSBF δ”1s”, and a trailing 0

4. 4 B0 B1 B2 B3 0 11110000 121111 11110000 11111100 000 00 1 111 3 items 2 items 1 item item Bit string HASH FUNCTION 3 bits 1 bit index Related work – blooming tree

5. 5 Outline Related work  Huffman spectral bloom filter  Blooming tree Minimal Perfect Hash Function  Using naïve blooming tree  Using optimized blooming tree and HSBF Experimental result

6. 6 MPHF – using NBT B0 B1 B2 B3 0 11010000 1111 111000 101110 00 00 1 1 1 item 2 items 1 item item Bit string HASH FUNCTION 3 bits 1 bit index Popcount is final hash number

7. 7 MPHF – using NBT B0 B1 B2 0 11010000 111000 101110 00 00 1 1 1 item 2 items 1 item Step1: Step2: final hash number = popcount item1 item2 item4 item3 hash 001 00 010 10 111 00 111 01 item1 item2 item4 item3 popcount 00 01 10 11 item1item2item3item4 B31111

8. 8 MPHF – using OBT and HSBT 0 11010000 010000 001 1 1 item 2 items 1 item 0000 B0 B1 B2 0 11010000 111000 101110 00 00 1 1 1 item 2 items 1 item NBTOBT

9. 9 MPHF – using OBT and HSBT 0 11010000 010000 001 1 1 item 2 items 1 item 0000 0 010000 001 1 2 items 1 item 0000 110 100 0 000 OBTOBT with HSBF

10. 10 MPHF – using OBT and HSBT Step1: Step2: final hash number = zero blocks item1 item2 item4 item3 Zero blocks 00 01 10 11 item1 item2 item4 item3 hash 001 000 010 100 111 000 111 010 … … 0 010000 001 1 1 item 2 items 1 item 0000 110 100 0 000

11. 11 MPHF – using OBT and HSBT Step1: Step2: final hash number = zero blocks item1 item2 item4 item3 Zero blocks 00 01 10 11 item1 item2 item4 item3 hash 001 000 010 100 111 000 111 010 … … 0 010000 001 1 1 item 2 items 1 item 0000 110 100 0 000 Start addr.Prev. elementsPrev. “10”s Y100 Y222 Lookup table : Y1 Y2

12. 12 MPHF – using OBT and HSBT Step1: Step2: final hash number = zero blocks item1 item2 item4 item3 Zero blocks 00 01 10 11 item1 item2 item4 item3 hash 001 000 010 100 111 000 111 010 … … 0 010000 001 1 1 item 2 items 1 item 0000 110 100 0 000 Start addr.Prev. elementsPrev. “10”s Y100 Y222 Lookup table : Y1 Y2 0

13. 13 Outline Related work  Huffman spectral bloom filter  Blooming tree Minimal Perfect Hash Function  Using naïve blooming tree  Using optimized blooming tree and HSBF Experimental result

14. 14 Experimental result Our  Intel 2.4Ghz Pentium 4 Core 2 Duo processor, 4GB RAM, Linux OS 2.6

15. 15 Experimental result BPZ  3.2 Ghz XEON, 1G RAM, Linux 2.6 BL  Pentium 4

16. 16

17. U U Bloom Filter 17 U U ite m1 ite m2 ite m 3 If present item in U as xxx Item1 can be 001 Item2 can be 010 Item3 can be 110 S S ite m1 ite m 3 There can be at most three items each present with three bits in set S. S can be present as 001 110 000

18. Bloom Filter 18 U U ite m 1 ite m 2 ite m 3 Assume hash function H(x) : H(item 1 ) = 0 H(item 2 ) = 1 H(item 3 ) = 2 U can be present in three bits, No.H(item i ) bit present i S can be present as 101 U U S S ite m1 ite m 3