1. HybridCuts: A Scheme Combining Decomposition and Cutting for Packet Classification Author: Wenjun Li, Xianfeng Li Publisher: 2013 IEEE 21 st Annual Symposium Presenter: Ching Hsuan Shih Date: 2013/12/11

2. Outline I. Introduction II. Background III. Related Work IV. HybridCuts V. Experimental Results

3. I. Introduction Two major approaches to packet classification: Architectural: TCAM Advantage: process packets at line speed Disadvantage: expensive, high power consumption, rule duplication Algorithmic: Decision-tree: Hicuts, HyperCuts, and EffiCuts Decomposition: BV

4. I. Introduction (Cont.) Proposed scheme: HybridCuts: a combination of decomposition and decision-tree techniques A rule set decomposition algorithm based on the observation that most rules have at least one small field. A novel one-dimensional cutting algorithm called FiCuts. A two-stage cutting framework which combines one-dimensional cutting and multi-dimensional cutting techniques.

5. II. Background A. The Packet Classification Problem To find a matching rule from a packet classifier for a packet. A classifier is a set of rules, with each rule R consisting of a tuple of F field values, and an action to be taken in case of a match.

6. II. Background (Cont.) B. Complexity in Theory From a geometric point of view, for N non-overlapping hyper- rectangles in F-dimensional space: The best bounds for locating a point are either Θ (log N) time with Θ (N F ) space, or Θ (log F-1 N) time with Θ (N) space. Impractical: with just 1000 rules and 4 fields, a solution is either impracticably (N F is about 1000G) or too slow (log F-1 N is about 1000 memory accesses).

7. II. Background (Cont.) C. Complexity in Practice It is infeasible to design a single algorithm that can perform well in all cases. Packet classification rules in real-life have some inherent characteristics that can be exploited to reduce the complexity. The protocol field is restricted to a small set of values. Rules specify a limited number of distinct transport port ranges. The number of address prefixes matching a given address is typically five or less. The number of rules matching a given packet is typically five or less. Many different rules share the same field values.

8. III. Related Work A. Parallel Bit-Vector (BV) One of most representative decomposition based solutions. It works on the individual fields of rules independently for partially matching results. Then a bit-wise AND operation on all bit vectors is performed to get the final result.

9. III. Related Work (Cont.)

10. B. HiCuts and HyperCuts Take a geometric view of the packet classification problem. HiCuts chooses one dimension to cut at one time. HyperCuts chooses multiple dimensions to cut at one time.

11. III. Related Work (Cont.) C. EffiCuts Separate rule set into several subsets, depending on whether the value of each dimension is wildcard (or almost wildcard). Each subset creates its own decision-tree independently using HyperCuts.

12. III. Related Work (Cont.) D. ParaSplit Employs a complex heuristic for rule set partitioning. It is different from EffiCuts in that its objective is for efficient hardware implementation using FPGAs.

13. IV. HybridCuts A. Decomposition-based Framework Definitions: Given an N-dimensional rule R = (F 1, F 2, F 3, …, F N ), Len i represents the length of field F i, and a threshold value vector T = (T 1, T 2, T 3, …, T N ). We call F i is a small field if Len i ≦ T i. Then we define the following concepts for R: Big rule: ∀ i ∈ {1, 2, 3... N}, F i in R is a big field Small rule: ∃ i ∈ {1, 2, 3... N}, F i in R is a small field

14. IV. HybridCuts (Cont.) We decompose a 5-tuple rule set into the following five subsets without duplicates among each other: 1. Big-subset: SA, DA, SP and DP are all big field 2. SA-subset: SA is a small field for each rule 3. DA-subset: DA is a small field for each rule 4. SP-subset: SP is a small field for each rule 2. DP-subset: DP is a small field for each rule When processing a rule R with two small fields: SA and DA, suppose the sizes of the SA-subset and the DA-subset up to now are N 1 and N 2 respectively, then rule R will go to SA-subset if N 1 ≦ N 2, or to DA-subset vice versa.

15. IV. HybridCuts (Cont.)

16. B. FiCuts: A One-Dimensional Cutting Technique Simplicity: FiCuts conducts cuttings on the subset along a fixed dimension Adaptivity: FiCuts can decide when to stop FiCuts and resort to other more effective cutting methods How to decide np: spfac * number of rules at node r ≥ ∑ number of rules at each child of node r + np

17. IV. HybridCuts (Cont.) binth = 4 spfac = 2

18. IV. HybridCuts (Cont.) C. Multi-dimensional Cutting With the shrinking of the search space, rule replications begin to rise with fine cuts. FiCuts makes the decision. If the number of cuts np at a node is less than a predefined MAXCUTS, FiCuts resorts to HyperCuts

19. IV. HybridCuts (Cont.) binth = 2 spfac = 2

20. IV. HybridCuts (Cont.) D. Optimization Most rules have at least one small IP address field (SA or DA). Based on this observation, we reduce the number of decision trees. For a 5-tuple rule set, we decompose it into three subsets: 1. Big-subset: Both SA and DA are big field 2. SA-subset: SA is a small field for each rule 3. DA-subset: DA is a small field for each rule

21. IV. HybridCuts (Cont.) Depends on SA, DA, SP, and DPDepends on SA, and DA

22. V. Experimental Results A. Memory Consumption

23. V. Experimental Results (Cont.) A. Memory Accesses

24. V. Experimental Results (Cont.) C. Potential of Parallelization It can be seen that in most cases, the worst-case height of a single tree is half of or less than the overall number of memory accesses on all the trees. This means that the trees constructed are balanced in height among each other, amenable to a parallel implementation with a potential 2x speedup.