1. 1 Layered Interval Codes for TCAM-based Classification Author: Anat Bremler-Barr, David Hay, Danny Hendler Publisher: IEEE INFOCOM 2009 Presenter: Chun-Yi Li Date: 2009/03/04

2. 2 Introduction  Range expansion was found to cause an increase of more than 16% in TCAM space requirements for real- word databases.  The algorithms we present split the ranges between multiple layers, each of which consists of mutually disjoint ranges.

3. 3 Introduction Minimum-space LIC (MLIC) The MLIC problem is to find a legal coloring C of G that minimizes The MLIC problem is to output a LIC code for the ranges of S that uses a minimum number of bits.

4. 4 Introduction Budgeted minimum LIC (BMLIC) The BMLIC problem is to find a subset V’ V and a coloring C of the subgraph of G induced by V’, such thatΣ w(v) is maximum under the constraint that C has LIC code-size of at most b.

5. 5 Introduction Encoding Example Liu’s basic dependent encoding

6. 6 Introduction Encoding Example LIC encoding

7. 7 Outline  The Layered Interval Encoding Scheme  Terminology  The Layering Stage  The Bits Allocation Stage  The Encoding Stage  Performance

8. 8 The Layered Interval Encoding Scheme Terminology  Minimum-space LIC (MLIC) The MLIC problem is to find a legal coloring C of G that minimizes The MLIC problem is to output a LIC code for the ranges of S that uses a minimum number of bits.

9. 9 The Layered Interval Encoding Scheme Terminology  Minimum-space LIC (MLIC) R4 R1 R2R3 R1 R2 R3 R4

10. 10 The Layered Interval Encoding Scheme Terminology  Budgeted minimum LIC (BMLIC) The BMLIC problem is to find a subset V’ V and a coloring C of the subgraph of G induced by V’, such thatΣ w(v) is maximum under the constraint that C has LIC code-size of at most b.

11. 11 The Layered Interval Encoding Scheme Terminology  Budgeted minimum LIC (BMLIC) An instance of BMLIC consists of a set S of weighted ranges and a positive integer b, the number of available bits. Under this restriction, it is required to output a LIC code for a maximum-weight subset S’ of S.

12. 12 The Layered Interval Encoding Scheme Terminology  weight – interval r’s total redundancy. Ex: R1 source port = [1,3] => 0001, 001* destination port = [9,12] => 1001, 101*, 1100 total redundancy = 2*3-1=5

13. 13 The Layered Interval Encoding Scheme The Layering Stage  Maximum Size Independent Sets (MSIS) This is a greedy layering algorithm that works iteratively. The algorithm finds a maximum size independent set.

14. 14 The Layered Interval Encoding Scheme The Layering Stage  Maximum Size Colorable Sets (MSCS) An i-colorable set of a graph G is a subset of G’s vertices that can be colored with i colors. MSCS finds a maximum size i- colorable set of G.

15. 15 The Layered Interval Encoding Scheme The Layering Stage  Maximum Size Colorable Sets (MSCS)

16. 16 The Layered Interval Encoding Scheme The Layering Stage  Maximum Weight Independent Sets (MWIS) Same as MSIS, except that we iteratively find a maximum weighted independent set.  Maximum Weight Colorable Sets (MWCS) Same as MSCS, except that, instead of finding maximum size k-colorable sets,MWCS finds maximum weight k-colorable sets.

17. 17 The Layered Interval Encoding Scheme The Bits Allocation Stage Compute the above quantity for each layer L i, and assign the next bit to a layer for which this quantity is maximal.

18. 18 The Layered Interval Encoding Scheme The Bits Allocation Stage Sort L i ’s interval in decreasing weight order

19. 19 The Layered Interval Encoding Scheme The Encoding Stage k 1 =assigned[m] k 2 = assigned[m] code[i][j] = * k 1 ． bin(j) ． * k 2 ‥‥ ‥‥‥‥‥‥ ‥‥‥‥‥‥‥ k 1 bits layer 1layer 2layer ilayer i+1 k 2 bits b bits layer n assigned[i] is the number of bits assigner to i’th layer

20. 20 Outline  The Layered Interval Encoding Scheme  Terminology  The Layering Stage  The Bits Allocation Stage  The Encoding Stage  Implementation Consideration  Supporting Multiple Range Fields  LIC Scheme Architecture  Hot Update Support  Performance

21. 21 Implementation Consideration Supporting Multiple Range Fields

22. 22 Implementation Consideration LIC Scheme Architecture

23. 23 Hot Update Support

24. 24 Outline  The Layered Interval Encoding Scheme  Terminology  The Layering Stage  The Bits Allocation Stage  The Encoding Stage  Performance

25. 25 Performance Expansion and redundancy factors, using 36 extra bits, for different range encoding algorithms.

26. 26 Performance The number of bits required to encode all the ranges that occur in our database as a function of the encoding scheme employed.

27. 27 Performance Redundancy factor as a function of the number of extra bits for different encoding schemes.

28. 28 Performance Redundancy factor as a function of the number of extra bits for different layering algorithms.