1. cs6390 summer 2000 Tradeoffs for Packet Classification 1 Tradeoffs for Packet Classification Members: Jinxiao Song & Yan Tong

2. cs6390 summer 2000 Tradeoffs for Packet Classification 2 Objectives To present an algorithm for solving the packet classification(PC) problem that allows various access time vs. memory tradeoffs concentrate on software solution for flow control: algorithm, data structure…etc

3. cs6390 summer 2000 Tradeoffs for Packet Classification 3 What’s the packet classification problem? Identifies the flow a packet belongs to, based on one or more fields in the packet header

4. cs6390 summer 2000 Tradeoffs for Packet Classification 4 How to classify the packets? packet header fields (dimensions) –destination and source IP addresses –protocol type –source and destination port numbers rules for classification –valid ranges for any of the header fields

5. cs6390 summer 2000 Tradeoffs for Packet Classification 5 Approaches to the problem multi-dimensional PC problem one-dimensional PC problem reduce dynamic PC problem static PC problem reduce

6. cs6390 summer 2000 Tradeoffs for Packet Classification 6 Requirements for packet classification Since this algorithm can be engineering to particular applications, so let find what is problem requirement from software engineering –Resource limitations tradeoff time to perform the classification per packet vs.memory used –Number of rules to be supported expect to scale up –Number of fields( dimensions ) used –Nature of rules some current routers use one field destination IP address

7. cs6390 summer 2000 Tradeoffs for Packet Classification 7 requirements (cont.) –Updating the set of rules the number of change to the rules either due to a route or policy change solutions must adapt gracefully and quickly to such updates without hurting access performance –Worse case vs.Average case –focus on worst case rather than average case

8. cs6390 summer 2000 Tradeoffs for Packet Classification 8 Problem specification given –a rule set R={ r 1,…,r n } of rules over d fields –each rule consists of ranges r i =[F i 1,..,F i d ] F i j is a range of values the field j may take –each rule with a cost –each query is a packet p={f 1,…,f d } where f i is a single value find –The least cost rule applies to the packet

9. cs6390 summer 2000 Tradeoffs for Packet Classification 9 What’s the key of authors’ algorithm? reduces the multi-dimensional packet classification problem to solving a few instances of the one-dimensional IP look up problem rules have a natural geometric interpretation in d-dimensions.

10. cs6390 summer 2000 Tradeoffs for Packet Classification 10 1-D 2-D 3D

11. cs6390 summer 2000 Tradeoffs for Packet Classification 11 What’s the one-dimensional PC problem? Given: –a set of n rules possibly overlapping intervals from [1…U] U-----the range of IP addresses –each rule with a cost

12. cs6390 summer 2000 Tradeoffs for Packet Classification 12 cont. find: –look up queries for point q  [ 1..U ] by identifying the smallest cost rule that contains q One dimensional PC problem has two special cases, they are bases for solving general one dimensional PC problem

13. cs6390 summer 2000 Tradeoffs for Packet Classification 13 Two special cases The IP Lookup(IPL) problem The Range Location(RL) problem

14. cs6390 summer 2000 Tradeoffs for Packet Classification 14 IP Look up problem( IPL ) classify packet based on the destination IP addresses each range is a prefix of an IP address goal:determine the least cost rule that is a prefix of q each query q is an IP address Basically, the IPL problem is giving a set of prefixes and address d(packet address), we want to find the longest matching prefix of d in routing table

15. cs6390 summer 2000 Tradeoffs for Packet Classification 15 Range Location problem( RL ) ranges are non-overlapping(elementary interval) completely cover the specified series of left end points of the intervals in the sorted order each query is an integer goal:determine the interval that contains q

16. cs6390 summer 2000 Tradeoffs for Packet Classification 16 Example: elementary intervals Elementary Intervals Ranges for rule

17. cs6390 summer 2000 Tradeoffs for Packet Classification 17 How to solve the RL? Reduce the RL to IPL based on a theorem: –Consider any instance I of the RL problem with N point in the range 1..U.We can derive an instance I’ of IPL with at most 2N prefixes,each a string of length at most a =  logU .Each query I for the PL problem can be transformed into an IP address of length at most a for the IPL problem on set I’

18. cs6390 summer 2000 Tradeoffs for Packet Classification 18 Example:reduction of RL to IPL 0000 0010 1000 1110 1111 RL problem: {0000, 0010, 1000, 1110, 1111}

19. cs6390 summer 2000 Tradeoffs for Packet Classification 19 RL  IPL cont. converted IPL problem with prefixes: {000x, 001x, 0xxx, 1xxx, 10xx, 11xx, 1110, 1111) routing table: prefixnext hop 0xxxR1 1xxxR4 10xxR5 11xxR8 000xR2 001xR3 1110R7 1111R6

20. cs6390 summer 2000 Tradeoffs for Packet Classification 20 Benefit of solution from RL to IPL used in the reduction: one-dimensional PC with arbitrary range rules  PC with only prefix while increasing the number of rules by at most a factor of two using the best known solutions for IPL to solve RL

21. cs6390 summer 2000 Tradeoffs for Packet Classification 21 Two - dimensional classification

22. cs6390 summer 2000 Tradeoffs for Packet Classification 22 What’s the two-dimensional PC problem? Given: a two-dimensional grid point q find : the smallest cost rectangle in R

23. cs6390 summer 2000 Tradeoffs for Packet Classification 23 1-D 2-D 3D

24. cs6390 summer 2000 Tradeoffs for Packet Classification 24 Data structure: FIS tree ( fat, inverted, segment tree ) data structure to support tradeoffs between access time and memory space S - a set of m segments t-ary tree l -level

25. cs6390 summer 2000 Tradeoffs for Packet Classification 25 FIS (cont.) balanced, inverted t-ary tree with l level leaves correspond to the elementary intervals in order larger interval is the union of the elementary intervals canonical set: the set of segments stored with a node

26. cs6390 summer 2000 Tradeoffs for Packet Classification 26 Properties of FIS the depth is log(m)/log(t) = l each segment is stored in at most 2t-1 nodes per level the collection of segments containing any point p is the union of l sets,the canonical subsets of the nodes on the search path of p in T; these sets are disjoint.

27. cs6390 summer 2000 Tradeoffs for Packet Classification 27 Preprocessing: according to 2-D PC problem construct: x-FIS tree y-set How to build the FIS tree

28. cs6390 summer 2000 Tradeoffs for Packet Classification 28 Example:construct of an x-FIS tree Elementary Intervals x-FIS tree 1 2 3 4 5 86 7 9 10 (3,4) (2,8,1) (9,10) 3-ary

29. cs6390 summer 2000 Tradeoffs for Packet Classification 29 Example:construct of the y-FIS tree of one node v 1 2 8 node v :canonical set (2,8,1) 5 x y

30. cs6390 summer 2000 Tradeoffs for Packet Classification 30 Query Processing: With 2-dimensional query point q = (q x, q y ) Reduce it to single instance of RL problem take advantage of the FIS tree Increase search speed

31. cs6390 summer 2000 Tradeoffs for Packet Classification 31 Steps for query processing Solve the RL problem on the x-set with query q x, get the leaf L x in the FIS tree representing the elementary interval containing q x Consider all successive parent of L x Search the y-sets associated with each parent of L x by solving the RL problem with q y for each nod. This determines the set of elementary interval that contain q from all y-sets. The smallest cost rectangle associated with these elementary intervals is returns as the solution.??? This can be thought of as solving the one-dimensional problem on the y-sets of the parents of L x, using FIS trees of only one level.

32. cs6390 summer 2000 Tradeoffs for Packet Classification 32 Theoretical results from query processing l-level x-FIS tree, n is the number of rules Memory space: O(ln 1+1/l ) Access time: (l+1)RL t (2n, U) The larger l is, the smaller the memory use and the larger the number of memory accesses

33. cs6390 summer 2000 Tradeoffs for Packet Classification 33 Multi-Dimensional classification construct a FIS tree on the first dimension and recursively construct our data structure on the remaining dimensions for each of the canonical sets in this FIS tree. The FIS TREE for the last dimension will be of level one just as in the two - dimensional case.

34. cs6390 summer 2000 Tradeoffs for Packet Classification 34 Dynamic PC problem: dynamic RL problem: at most twice the number of memory access as the solution to the static RL problem. (the penalty can be avoided by using a cacheline twice as wide). incremental classification: relax the degree of the FIS tree, dynamic classification: relax the delta canonical set of node and the degree of the FIS tree dynamic PCdynamic RL insert (incremental classification)split delete(dynamic classification)merge

35. cs6390 summer 2000 Tradeoffs for Packet Classification 35 Example:construct of an x-FIS tree Elementary Intervals x-FIS tree 1 2 3 4 5 86 7 9 10 (3,4) (2,8,1) (9,10) 3-ary

36. cs6390 summer 2000 Tradeoffs for Packet Classification 36 Principle for solving dynamic PC : Make data structure(FIS tree) flexible but not destroy its global stability: dynamic PC  dynamic RL  static RL relax the degree of the FIS tree:the cost of lookup remains essential unchanged while increase the use of memory maintain the current data structure so that delta canonical sets are small incremental classification: incremental FIS tree

37. cs6390 summer 2000 Tradeoffs for Packet Classification 37 Various Tradeoffs in classification: static PC problem: the larger l (levels of FIS tree) is, the small the memory use and the larger the number of memory access will be choose appropriate solutions for the subproblems the order in which the dimensions must be considered

38. cs6390 summer 2000 Tradeoffs for Packet Classification 38 Additional considerations for dynamic PC problem: choice of the branching factor. multiplex the updating of the tree with performing the lookups, although this requires careful implementation. batch updates and perform them more efficiently than doing each individual update separately.

39. cs6390 summer 2000 Tradeoffs for Packet Classification 39 Experimental study: algorithms tested performance metrics:measuring the memory accesses, measuring the memory usage For small rulesets (up to a few K rules), one level FIS tree suffices. The space used is a few 100k bytes and the number of memory accesses is less than 10. For few 10 K rules, 2 level FIS tree, space is a few Mbytes, memory access is about 15. For very large dataset(10^6 rules), 2-3 level FIS tree, space 100 Mbytes, memory access is up to 18

40. cs6390 summer 2000 Tradeoffs for Packet Classification 40 Related work: Many research in this area Motivation is to explore if software based solutions can perform lookups at high linespeed.

41. cs6390 summer 2000 Tradeoffs for Packet Classification 41 Conclusions: 1.Using a “fat” hierarchy of canonical sets to decrease the number of sets to be searched per query 2.Locating the canonical sets to be searched by processing up from the leaves using the inverted edges of FIS tree 3.Locating the leaves in FIS trees using the standard IPL problem, thereby leveraging off best known hardware and software solutions for it 4.Using FIS tree nodes with flexible degree to allow moderate number of updates without degrading the lookup performance significantly 5.Reducing the universe size using IPL problem before applying our solutions thereby reducing the memory accesses for each consequent IPL solution