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

4 B0 B1 B2 B items 2 items 1 item item Bit string HASH FUNCTION 3 bits 1 bit index Related work – blooming tree

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 MPHF – using NBT B0 B1 B2 B item 2 items 1 item item Bit string HASH FUNCTION 3 bits 1 bit index Popcount is final hash number

7 MPHF – using NBT B0 B1 B item 2 items 1 item Step1: Step2: final hash number = popcount item1 item2 item4 item3 hash item1 item2 item4 item3 popcount item1item2item3item4 B31111

8 MPHF – using OBT and HSBT item 2 items 1 item 0000 B0 B1 B item 2 items 1 item NBTOBT

9 MPHF – using OBT and HSBT item 2 items 1 item items 1 item OBTOBT with HSBF

10 MPHF – using OBT and HSBT Step1: Step2: final hash number = zero blocks item1 item2 item4 item3 Zero blocks item1 item2 item4 item3 hash … … item 2 items 1 item

11 MPHF – using OBT and HSBT Step1: Step2: final hash number = zero blocks item1 item2 item4 item3 Zero blocks item1 item2 item4 item3 hash … … item 2 items 1 item Start addr.Prev. elementsPrev. “10”s Y100 Y222 Lookup table : Y1 Y2

12 MPHF – using OBT and HSBT Step1: Step2: final hash number = zero blocks item1 item2 item4 item3 Zero blocks item1 item2 item4 item3 hash … … item 2 items 1 item Start addr.Prev. elementsPrev. “10”s Y100 Y222 Lookup table : Y1 Y2 0

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

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

16

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

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