1. 1 Efficient Packet Classification using Splay Tree Models Author: Srinivasan.T, Nivedita.M, Mahadevan.V Publisher: IJCSNS International Journal of Computer Science and Network Security 2006 Presenter: Hsin-Mao Chen Date:2010/05/19

2. 2 Outline Introduction Splay Trees ST-PC Technique Search Complexity Analysis

3. 3 Introduction Splay Tree based Packet Classification (ST-PC) 1. Splay tree 2. Prefix conversion

4. 4 Splay Trees Splay trees are self-balancing or self- adjusting binary search trees. When we access a node of the tree (retrieval, insertion, deletion), it performs radical surgery on the tree. Splay trees does not require height or balance factors as in AVL trees and colors as in Red-Black trees.

5. 5 Splay Trees

6. 6 There are six rotations possible in a splay tree: 1. Zig Rotation 2. Zag Rotation 3. Zig-Zig Rotation 4. Zag-Zag Rotation 5. Zig-Zag Rotation 6. Zag-Zig Rotation

7. 7 Splay Trees g p x

8. 8 Zig Rotation p x a b c x a b c p

9. 9 Splay Trees Zig-Zig Rotation g p x c d ab x a b g p c d

10. 10 Splay Trees Zig-Zag Rotation g p a x d bc p ab g cd x

11. 11 ST-PC Technique

12. 12 ST-PC Technique [0,15] [16,16] [17,31] [32,32] [33,47] [48,63]

13. 13 ST-PC Technique [0,15] [16,16] [17,31] [32,32] [48,63] [33,47]

14. 14 ST-PC Technique

15. 15 Search [17,31] [0,15][33,47] [16,16] [32,32] [48,63] [0,15] [16,16] [17,31] [33,63] F5, F6 [32,32]

16. 16 Complexity Analysis Binary Trie: All the prefix are distinct: 2 k+1 -1 All k bits of each of the r rules are distinct: (k * r)+1 Splay Tree: All the prefix: 2 k All rule are distinct: 2*r

17. 17 Complexity Analysis

18. 18 Complexity Analysis

19. 19 Complexity Analysis m unique accesses Binary Trie: m*log(2n) Splay Tree: m*log(n) (m-t) unique accesses Binary Trie: m*log(2n) Splay Tree: ((m-t)log(n)) + t*log(β)

20. 20 Complexity Analysis

21. 21 Complexity Analysis