1. SCALAR PREFIX SEARCH: A NEW ROUTE LOOKUP ALGORITHM FOR NEXT GENERATION INTERNET Author: Mohammad Behdadfar, Hossein Saidi, Hamid Alaei and Babak Samari Publisher/Conf.: INFOCOM 2009. The 28th Conference on Computer Communications. IEEE Speaker: Han-Jhen Guo Date: 2009.06.17 1

2. OUTLINE Introduction Related Work Proposed scheme Scalar Prefix Search Binary Search Tree (SP- BST) Scalar Prefix Search B-Tree (SP-BT) Scalar Prefix Search B-Tree Enhance (SP-BTe) Performance 2

3. INTRODUCTION 3

4. RELATED WORK Comparison of Scalar Prefixes eg. P 2 = 010*, P 3 = 011* 010 < 011 → P 2 < P 3 eg. P 1 = 01*, P 2 = 010* 01 = 01, len(P 1 ) < len(P 2 ) → P 1 < P 2 4

5. PROPOSED SCHEME prefix → scalar prefix ( match vector, key ) eg.(len. of IP addr.= 4 ) 01* → ( 0100, 0100 ) (cont.) 010* → ( 0110, 0100 ) 5 0100, 010001* 010* 0110, 0100

6. PROPOSED SCHEME - SCALAR PREFIX SEARCH BINARY SEARCH TREE (SP-BST) Insertion (Creation) eg. (len. of IP addr.= 4 ) ins. P 1 = 0* 1000, 0000 6 0*

7. 1000, 0000 PROPOSED SCHEME - SCALAR PREFIX SEARCH BINARY SEARCH TREE (SP-BST) Insertion (Creation) eg. (cont.) ins. P 2 = 01* 1100, 0100 7 01* covers P 2 0*0*, 01*

8. PROPOSED SCHEME - SCALAR PREFIX SEARCH BINARY SEARCH TREE (SP-BST) Insertion (Creation) eg. (cont.) ins. P 3 = 000* 1100, 0100 8 01* and P 3 are disjoint P 3 < 01* → left 0010, 0000 0*, 01* 000*

9. PROPOSED SCHEME - SCALAR PREFIX SEARCH BINARY SEARCH TREE (SP-BST) Insertion (Creation) eg. (cont.) ins. P 4 = 001* 1100, 0100 9 01* and P 4 are disjoint P 4 < 01* → left 0010, 0000 000* and P 4 are disjoint P 4 > 000* → right 0010, 0010 0*, 01* 000* 001*

10. PROPOSED SCHEME - SCALAR PREFIX SEARCH BINARY SEARCH TREE (SP-BST) Deletion eg. (len. of IP addr.= 4 ) del. P = 00* 1100, 0100 10 01* and P are disjoint P < 01* → left 0110, 0000 0010, 0010 0100, 1000 000* covers P key ≠ key(P) 0010, 0000

11. PROPOSED SCHEME - SCALAR PREFIX SEARCH BINARY SEARCH TREE (SP-BST) Deletion eg. (cont.) del. P = 000* 1100, 0100 11 0010, 0000 0010, 0010 0100, 1000 key ＝ key(P) ONLY 1 prefix in this node do deletion of BST 01* and P are disjoint P < 01* → left

12. 1010, 0010 PROPOSED SCHEME - SCALAR PREFIX SEARCH BINARY SEARCH TREE (SP-BST) Deletion eg. (len. of IP addr.= 4 ) del. P = 001* 0100, 1000 12 01* and P are disjoint P < 01* → left 0110, 0110 0100, 11001000, 0000 key ＝ key(P) NOT only 1 prefix in this node may be pulled up after update the m.v. with the colored node of the path 0010, 0100 successor (predecessor) 1000, 0000 0110, 0110 1000, 0000 0010, 0100 0000, 0000 1010, 0100 0110, 01100010, 0110 1110, 0100

13. PROPOSED SCHEME - SCALAR PREFIX SEARCH BINARY SEARCH TREE (SP-BST) Conclusion the average search time would be reduced the average height of the tree is reduced the average storage requirement would be reduced prefixes are stored in one key and also this tree doesn’t need to store both of the prefix end points 13

14. PROPOSED SCHEME - SCALAR PREFIX SEARCH B-TREE (SP-BT) Decrease the worst case memory access time of SP-BST worst case memory access for lookup and update procedures = O(log n) Definition of SP-BT key of B-tree are in the form of pair of ( match vector, key ) 14

15. PROPOSED SCHEME - SCALAR PREFIX SEARCH B-TREE (SP-BT) Split in case of insertion eg. ins. P = 10110 15 0000* 111* 1* 1000* 100* 10010 1001* 10011 10101 10111 10011 100* (A) 1001* (B) 1* (X) 10011 100* (A) 1001* (B) 1* (X) C may be updated by A, B and X

16. PROPOSED SCHEME - SCALAR PREFIX SEARCH B-TREE (SP-BT) Borrow in case of deletion 16 D may be updated by B and C X, Y and Z may be updated by B D may be updated by B and C X, Y and Z may be updated by B

17. PROPOSED SCHEME - SCALAR PREFIX SEARCH B-TREE (SP-BT) Merge in case of deletion 17 C may be updated by B Y and Z may be updated by B C may be updated by B Y and Z may be updated by B

18. PROPOSED SCHEME - SCALAR PREFIX SEARCH B-TREE ENHANCE (SP-BTE) Difference between SP-BT and SP-BTe 18

19. PERFORMANCE Implemented with three types of balanced trees: B-tree, RB-tree and AVL-tree The B-Tree degree = 14 and 8 Databases R100 and R500 2 random databases of 100000 and 500000 prefixes respectively with the current prefix lengths distribution of IPv4 prefixes AS4637 and AS1221 2 BGP tables, 139519 prefixes and 191566 prefixes respectively 19

20. PERFORMANCE Search time 20

21. PERFORMANCE Update time 21

22. PERFORMANCE Memory consumption 22

23. PERFORMANCE The results of applying a random database with 50% disjoint prefixes 23

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