Author : Hyuntae PARK, Hyejeong HONG and Sungho KANG Publisher: IEICE TRANS. COMMUN. 2011

1. An Efficient IP Address Lookup Scheme Using Balanced Binary Search with Minimal Entry and Optimal Prefix Vector Author: Hyuntae PARK, Hyejeong HONG and Sungho KANG Publisher: IEICE TRANS. COMMUN. 2011 Presenter: Li-Hsien, Hsu Data: 12/28/2011

2. Introduction • We propose an efficient binary search algorithm for IP address lookup in the Internet routers. • We propose a perfectly balanced search algorithmbased on the binary search tree. • To preform the binary search properly, the BST algorithm strictly restricts that the enclosure prefix is stored in a higher level than its enclosed prefix so that the enclosure is compared earlier, and this restriction makes the binary search tree highly unbalanced in case that are many levels of prefix nesting.

3. P2 Introduction P3 P4 • To construct a balanced binary search tree, we remove the prefix nesting relationship of nodes in the binary search tree and make each node hold a prefix vector containing the nesting information. • Definition: • Leaf prefixes of the binary trie. Ex：P0,P1,P2, P5, P6, P7 or P9 P8 P0 P1 P7 P9 P5 P6

4. P2 Introduction P3 P4 • What is the prefix vector? Ex： The prefix vector of P1 is [Y3, ø, ø, Y1, ø] The prefix vector of P2 is [Y3, ø, ø, Y2, ø] The prefix vector of P5 is [Y4, Y8, ø, ø, Y5] The prefix vector of P6 is [Y4, Y8, ø, ø, Y6] The prefix vector of P7 is [Y4, Y8, ø, Y7, ø] P8 P0 P1 P7 P9 P5 P6

5. P2 Introduction P3 P4 • What is the prefix vector? Ex： The prefix vector of P1 is [Y3, ø, ø, Y1, ø] The prefix vector of P2 is [Y3, ø, ø, Y2, ø] The prefix vector of P5 is [Y4, Y8, ø, ø, Y5] The prefix vector of P6 is [Y4, Y8, ø, ø, Y6] The prefix vector of P7 is [Y4, Y8, ø, Y7, ø] P8 P0 P1 P7 P9 P5 P6

6. P2 Definition(1/3) P3 P4 S(Px,j) : sub-string of the most significant j bits of prefix Px. L(Px): length of prefix Px. V(Px):the prefix vector of Px V(Px): the k-th vector element in V(Px) P8 P0 P1 P7 P9 P5 P6

7. P2 Definition(2/3) P3 P4 S(Px,j) : sub-string of the most significant j bits of prefix Px. L(Px): length of prefix Px. V(Px):the prefix vector of Px V(Px): the k-th vector element in V(Px) P8 P0 P1 P7 P9 P5 P6

8. P2 Definition(3/3) P3 P4 S(Px,j) : sub-string of the most significant j bits of prefix Px. L(Px): length of prefix Px. V(Px):the prefix vector of Px V(Px): the k-th vector element in V(Px) P8 P0 P1 P7 P9 P5 P6

9. P2 P3 P4 P8 P0 P1 P7 P9 P5 P6

10. P4 P2 P3 P4 P3 P8 P8 PM1 P0 P1 P7 P7 P5 P9 P5 P6 P9 P6 gray node: ordinary or iso-likeness prefixes. black node: likeness prefixes.

11. Search(1/5) • Incoming address: 11001 • best matching prefix length: 0 • corresponding output port of the BMP: default

12. Search(2/5) • Incoming address: 11001 • best matching prefix length: 0 • corresponding output port of the BMP: default

13. Search(3/5) • Incoming address: 11001 • best matching prefix length: 2 • corresponding output port of the BMP:Y8

14. Search(4/5) • Incoming address: 11001 • best matching prefix length: 2 • corresponding output port of the BMP:Y8

15. Search(5/5) • Incoming address: 11001 • best matching prefix length: 4 • corresponding output port of the BMP:Y6

16. Performance Evaluation • The number of entries in each scheme Ne • The average numbers of memory accesses Tav • The maximum numbers of memory accesses Tmx • The required memory size M