1. A SPACE- AND TIME-EffiCIENT HASH TABLE HIERARCHICALLY INDEXED BY BLOOM FILTERS
Author: Heeyeol Yu and Rabi Mahapatra
Publisher/Conf.: Parallel and Distributed Processing, IPDPS IEEE International Symposium on
Speaker: Han-Jhen Guo
Date:

2. OUTLINE The Proposed Scheme Performance Concept Insertion Query
Modification
Deletion
Performance
Simulation for IP Lookup
Time Complexity
Memory Consumption

3. THE PROPOSED SCHEME - CONCEPT
Basic configuration of hierarchical indexing tree of 0- and 1-tree

4. THE PROPOSED SCHEME - CONCEPT
Hierarchically Indexed Hash Table (HIHT)
Assumption
hash functions are perfectly random
n keys → s = log2(n) layers (SRAM modules)
at same level i, each BF use mi-bit vector and ki hash functions
The BFs in the hierarchical indexing tree (HIT) used for indexes to a key table is hierarchically partitioned to make indexes

5. THE PROPOSED SCHEME - INSERTION
(eg. insert key = 011, rule = E, addr(key) = 4)
1-3. set all k1 m1-bit vectors
with hi(key) in parallel
(0 <= i <= k1-1)
1-1. base addr = 100 * m1 * k1
key table
rule table

6. THE PROPOSED SCHEME - INSERTION
(eg. insert key = 011, rule = E, addr(key) = 4)
2-3. set all k2 m2-bit vectors
with hi(key) in parallel
(0 <= i <= k2-1)
2-1. base addr = 100 * m2 * k2
key table
rule table

7. THE PROPOSED SCHEME - INSERTION
(eg. insert key = 011, rule = E, addr(key) = 4)
3-3. set all k3 m3-bit vectors
with hi(key) in parallel
(0 <= i <= k3-1)
3-1. base addr = 100 * m3 * k3
key table
rule table

8. THE PROPOSED SCHEME - INSERTION
(eg. insert key = 011, rule = E, addr(key) = 4)
011
key table E
rule table

9. THE PROPOSED SCHEME - QUERY
No f-positive (eg. search key = )
calculate hi(key) in parallel (0 <= i <= k1-1 )
count 1’s = k1 → hit;
A = 1
000
001
010
110
011
100
101
111
key table A B C D E F G H
rule table

10. THE PROPOSED SCHEME - QUERY
No f-positive (eg. search key = )
calculate hi(key) in parallel (0 <= i <= k2-1 )
count 1’s = k2 → hit;
A = 10
000
001
010
110
011
100
101
111
key table A B C D E F G H
rule table

11. THE PROPOSED SCHEME - QUERY
No f-positive (eg. search key = )
calculate hi(key) in parallel (0 <= i <= k3-1 )
count 1’s = k3 → hit;
A = 100
000
001
010
110
011
100
101
111
key table A B C D E F G H
rule table

12. THE PROPOSED SCHEME - QUERY
No f-positive (eg. search key = )
A = 100
000
001
010
110
011
100
101
111
key table
key is matched A B C D E F G H
rule table

13. THE PROPOSED SCHEME - QUERY
No f-positive (eg. search key = )
000
001
010
110
011
100
101
111
key table A B C D E F G H
rule table
fetch relative rule

14. THE PROPOSED SCHEME - QUERY
F-positive (eg. search key = )
000
001
010
110
011
100
101
111
key table A B C D E F G H
rule table

15. THE PROPOSED SCHEME - QUERY
No f-positive (eg. search key = )
A = 010
A = 100
000
001
010
110
011
100
101
111
key table
key is unmatched
key is matched A B C D E F G H
rule table

16. THE PROPOSED SCHEME - QUERY
No f-positive (eg. search key = )
000
001
010
110
011
100
101
111
key table A B C D E F G H
rule table
fetch relative rule

17. THE PROPOSED SCHEME - MODIFICATION
Dual HITs
valid bit array (VBA)
on-chip; indicate whether the key exists in the key table
next
on-chip; indicate the address for inserting next new key
free address stack (FAS)
off-chip; store addresses of empty spaces

18. THE PROPOSED SCHEME - DELETION
No f-positive (eg. delete key = 011)
next
100
FAS
100 1
VBA
000
001
010
110
011
100
101
111 A B C D E F G H

19. THE PROPOSED SCHEME - DELETION
F-positive (eg. delete key = 001)
100
next
001
100
FAS
001 1
VBA
000
001
010
110
100
101
111
f-positive is checked by unmatched key
f-positive is checked A B C D F G H

20. THE PROPOSED SCHEME - INSERTION
(eg. insert key = 101, r = G)
110
next
001
001
100
FAS 1
VBA 1
000
010
110
100
111
101 A C D F H G

21. Performance - Simulation for IP Lookup
Architecture

22. PERFORMANCE - SIMULATION FOR IP LOOKUP
Related work - Prefix collapsing
(eg. collapse stride = 3)

23. PERFORMANCE - TIME COMPLEXITY
Average access time to a table or a linked list as a function of SS rate

24. PERFORMANCE - MEMORY COMSUMPTION
On-chip memory size with various hash schemes for 6 BGP tables in 40Gbps and 160Gbps routers
table
# of prefixes B1
AS65000
233451 B2
AS6447
235307 B3
AS1221
181295 B4
AS12654
170459 B5
AS5459
78133 B6
AS3303
68739
160Gbps: 4.5 and 2.0 times efficiency over a c-FHT and a BFHT
40Gbps: 4.2 and 2.0 times efficiency over a c-FHT and a BFHT

25. Thanks for
your listening!