1. 1 Compressing Two-Dimensional Routing Tables Author: Subhash Suri, Tuomas Sandholm, Priyank Warkhede. Publisher: ALGO'03 Presenter: Yu-Ping Chiang Date: 2009/03/11

2. 2 Outline Previous work One dimension compression Two dimension compression Experimental results

3. 3 Previous work Definition :  Think as a prefix rectangle with color i.  Point is assigned the smallest rectangle’s color. Constraint : Consistent  Rules are disjoint or nested

4. 4 Previous work Target : Determine the smallest set of consistent prefix rectangles and their colors that induce the same coloring as the input set.

5. 5 Outline Previous work One dimension compression Two dimension compression Experimental results

6. 6 One dimension compression Smallest equivalent prefix set Dynamic programming Background prefix  Prefix range is whole interval NOT OPTIMAL!!

7. 7 One dimension compression For all prefix s compute  is the list of background colors that give the minimum cost solutions. .. .

8. 8 One dimension compression Initialize output list to root prefix s, and give it background color c, for any. If, add a new prefix s0 with any color, recurse L(s0) with background color c’. Else, recurse L(s0) with background color c. Similarly in L(s1). Worst case time and space complexity: O(NKw). N = # of filter entry K = # of colors (distinct routing action) w = field length (bits)

9. 9 Original prefix set:

10. 10 Original prefix set:

11. 11

12. 12 Outline Previous work One dimension compression Two dimension compression Experimental results

13. 13 Two dimension compression ‧ R’ = ( s’, d’ ) spans R = ( s, d ) alone s-axis means s=s’ and d is prefix of d’.

14. 14 Two dimension compression

15. 15 Outline Previous work One dimension compression Two dimension compression Experimental results

16. 16 Experimental result One dimension compression Implemented on 300MHz Pentium II running on Windows NT. Number of prefixes : 8000~41000 Colors (distinct next hops) : 17~58

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18. 18 Proof.

19. 19 Proof. back