1. A Memory-Efficient Hashing by Multi-Predicate Bloom Filters for Packet Classification
Author: Heeyeol Yu; Mahapatra, R.;
Publisher: IEEE INFOCOM 2008
Presenter: Yu-Ping Chiang
Date: 2008/12/17

2. Outline Related Works – Basic Bloom filter
Multi-predicate Bloom-filter Hash Table (MBHT)
Benefits
Architecture
Insert
Query
Delete
Analysis and Simulation
On/Off-chip memory usage
Average access of search
URL switching

3. Related Works – Basic Bloom filter
set S =
n elements.
represented in m bits array, initially set to 0.
using k independent hash functions mapping. ……
………………… …… 1 2 3
m-1

4. Related Works – Basic Bloom filter
The probability that a bit is 0
Probability of false-positive
In requirement of
by [17] A. Broder and M. Mitzenmacher, “Network Applications of Bloom Filters: A Survey,” pp. 485–509, [Online]. Available:citeseer.ist.psu.edu/broder02network.html

5. Related Works – Basic Bloom filter
Linear property
Given f, n is linearly proportionate to m.
Reverse Exponential Property
Given n, m is exponential effect on f.

6. Outline Related Works – Basic Bloom filter
Multi-predicate Bloom-filter Hash Table (MBHT)
Benefits
Architecture
Insert
Query
Delete
Analysis and Simulation
On/Off-chip memory usage
Average access of search
URL switching

7. MBHT - Benefits On-chip Off-chip
Reduce memory size in base- number system by x times compares to that of base- number system.
Insert and delete operations are done in constant time in parallel.
Off-chip
Saves memory by removing linked list mechanism.
Does not save the duplicate items.

8. MBHT - Architecture 01

9. MBHT - Insert Partition address space. n elements
Base-b number system,
→ digits
Address with r digits of x bits :
is covered by

10. MBHT - Insert

11. MBHT - Insert Transform to base-4 number system
Fewer columns in each address space.
Not affect addressing off-chip memory.

12. MBHT - Insert
Memory usage : .

13. MBHT - Insert Memory change rate with f and n.
→larger base is advantageous because x times on-chip memory saving.
(hard in real hardware.)

14. MBHT - Insert Algorithm : → Θ(1) → Θ(1) Execute each column
Set bloom filter
→ Θ(1)

15. MBHT - Query Algorithm Consider only on-chip operation.
Need to be called twice on l-MBHT and r-MBHT
Θ(1)

16. MBHT - Delete Algorithm Need to be called twice on l-MBHT and r-MBHT
Θ(1)

17. Outline Related Works – Basic Bloom filter
Multi-predicate Bloom-filter Hash Table (MBHT)
Benefits
Architecture
Insert
Query
Delete
Analysis and Simulation
On/Off-chip memory usage
Average access of search
URL switching

18. On/Off-chip memory usage
R = # of layers
B = # of bits in one layer
(in FHT memory consumption, 4 is bits for counter.)
Memory efficiency ratio :

19. On/Off-chip memory usage
Better memory efficiency ratio begins at b =

20. Average access of search
The lower successful search rate,
the better access time performance

21. URL switching on-chip memory reduction 1.7 times to LHT 2 times to FHT
AAS* = average access for a successful search