# Data Structures for Packet Classification

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1 Presenter: Patrick Nicholson Department of Computer Science CS840 Topics in Data Structures

2 Outline 1 The Problem 2 Hardware Solutions 3 Data Structures: 1D 4 Trie-Based Solutions

3 Packet Classification Problem: Internet routers must be able to forward packets according to increasingly sophisticated schemes, and also at higher speeds

4 Packet Classification Problem: Internet routers must be able to forward packets according to increasingly sophisticated schemes, and also at higher speeds Past: forward packets based only on destination (best effort).

5 Packet Classification Problem: Internet routers must be able to forward packets according to increasingly sophisticated schemes, and also at higher speeds Past: forward packets based only on destination (best effort). Now: next hop is determined based on more information, for quality of service purposes.

6 Definitions/Examples: Definition Packet: A 5-tuple consisting of source/destination address, source/destination port, and protocol. Example P = ( , , 4444, 21, TCP)

7 Definitions/Examples: Definition Filter or Rule: A 5-tuple that describes one or more packets. Example F = ( , , [0 : 5000], [20 : 22], )

8 Definitions/Examples: Definition Classifier: A table that maps filters to actions, where each filter has a priority. For our purposes, we will assume priorities are unique. Example Filter Action ( , , [0 : 5000], [20 : 22], UDP) flow 3 ( , , 21, 80, TCP) drop ( ,, 22, 22, ) flow 10

9 Notation: N - number of filters in the classifier

10 Notation: N - number of filters in the classifier W - the maximum number of bits used by a classifier field (IPv4 = 32)

11 Notation: N - number of filters in the classifier W - the maximum number of bits used by a classifier field (IPv4 = 32) d - the number of fields in the classifier (typically 5)

12 Hardware Solution: CAMS Modern routers use Ternary Content Addressable Memory (TCAM).

13 Hardware Solution: CAMS Modern routers use Ternary Content Addressable Memory (TCAM). Think of it as inverted RAM: you supply the content, and it supplies the memory address.

14 Hardware Solution: CAMS Modern routers use Ternary Content Addressable Memory (TCAM). Think of it as inverted RAM: you supply the content, and it supplies the memory address. It is fast, but has high cost and also takes a lot of power since it is doing comparisons brute force style in parallel.

15 Hardware Solution: CAMS Modern routers use Ternary Content Addressable Memory (TCAM). Think of it as inverted RAM: you supply the content, and it supplies the memory address. It is fast, but has high cost and also takes a lot of power since it is doing comparisons brute force style in parallel. Can we reduce cost by using data structures stored in SRAM?

16 When d = 1: Longest Prefix Matching If we handle the packet based only on destination address, the problem is simply that of longest prefix matching.

17 When d = 1: Longest Prefix Matching If we handle the packet based only on destination address, the problem is simply that of longest prefix matching. Degermark et al. (1997) Small Forwarding Tables for Fast Routing Lookups

18 When d = 1: Longest Prefix Matching If we handle the packet based only on destination address, the problem is simply that of longest prefix matching. Degermark et al. (1997) Small Forwarding Tables for Fast Routing Lookups Trie represented by bit-vectors and look-up tables: typical search req. eight memory accesses.

19 When d = 1: Longest Prefix Matching If we handle the packet based only on destination address, the problem is simply that of longest prefix matching. Degermark et al. (1997) Small Forwarding Tables for Fast Routing Lookups Trie represented by bit-vectors and look-up tables: typical search req. eight memory accesses. Alternatively: Waldvogel et al. (1997) Scalable High Speed IP Routing Lookups, uses binary search on prefixes to get O(log W ) search time...

20 When d = 1: Longest Prefix Matching If we handle the packet based only on destination address, the problem is simply that of longest prefix matching. Degermark et al. (1997) Small Forwarding Tables for Fast Routing Lookups Trie represented by bit-vectors and look-up tables: typical search req. eight memory accesses. Alternatively: Waldvogel et al. (1997) Scalable High Speed IP Routing Lookups, uses binary search on prefixes to get O(log W ) search time... But really it s the same as Q1 of our first assignment, i.e. Willard (1983).

21 Algorithms/Data Structures: d > 1 We can think of the problem in higher dimensions as the geometric problem of finding the highest priority hyper-rectangle. Here is an example for d = 2.

22 Algorithms/Data Structures: d > 1 We can think of the problem in higher dimensions as the geometric problem of finding the highest priority hyper-rectangle. Here is an example for d = 2. R S D 1 00* 11* 2 01 * * 3 10* 00* 4 11* 00* * 6 * * 01* 8 010* 10* * Destination ([0 : 15]) R1 R2 R3 R4 R5 R8 R6 R7 R6 Source ([0 : 15])

23 Algorithms/Data Structures: d > 1 There is no shortage of algorithms for solving this problem: HiCuts, Aggregate Bit Vectors, Recursive Flow Classification, etc.

24 Algorithms/Data Structures: d > 1 There is no shortage of algorithms for solving this problem: HiCuts, Aggregate Bit Vectors, Recursive Flow Classification, etc. In this talk we will cover trie-based solutions, starting with the 2D example from the last slide.

25 Hierarchical Trie R S D 1 00* 11* 2 01 * * 3 10* 00* 4 11* 00* * 6 * * 01* 8 010* 10* * Source Destination R6 R2 R3 R9 R2 R7 R2 R2 R8 R5 R2 R8 R5 R2 R5 R1 R1 R2 R5 R2 R5 R4

26 Hierarchical Trie: search for 1111/0101 R S D 1 00* 11* 2 01 * * 3 10* 00* 4 11* 00* * 6 * * 01* 8 010* 10* * R5

27 Hierarchical Trie: observations Problem: Searching is O(W ) (good), but memory is clearly O(N 2 ) which is unacceptable.

28 Set Pruning Trie with Backtracking R S D 1 00* 11* 2 01 * * 3 10* 00* 4 11* 00* * 6 * * 01* 8 010* 10* * Source Destination R3 R9 R7 R2 R6 R8 R5 R1 R4

29 Set Pruning Trie with Backtracking: search for 1111/0101 R S D 1 00* 11* 2 01 * * 3 10* 00* 4 11* 00* * 6 * * 01* 8 010* 10* * R5 0

30 Set Pruning Trie with Backtracking: observations Problem: Memory is now O(NW ) (good), but searching is O(W 2 ) (not so good).

31 Set Pruning Trie with Backtracking: observations Problem: Memory is now O(NW ) (good), but searching is O(W 2 ) (not so good). Solution: Add extra pointers.

32 Grid-of-Tries (Srinivasan et al 1998) R S D 1 00* 11* 2 01 * * 3 10* 00* 4 11* 00* * 6 * * 01* 8 010* 10* * Source Destination R3 R9 R7 R2 R6 R8 R5 R1 R4

33 Grid-of-Tries: search for 1111/0101 R S D 1 00* 11* 2 01 * * 3 10* 00* 4 11* 00* * 6 * * 01* 8 010* 10* * R5 1 0

34 Grid-of-Tries: observations Memory is now O(NW ) (good), and searching is O(W ) (also good). Additionally, since the destination trie is never visited again after finding the longest prefix, we can use any scheme we like for the top half of the trie. However...

35 Grid-of-Tries: observations Memory is now O(NW ) (good), and searching is O(W ) (also good). Additionally, since the destination trie is never visited again after finding the longest prefix, we can use any scheme we like for the top half of the trie. However... This scheme really only works in 2D:

36 Grid-of-Tries: observations Memory is now O(NW ) (good), and searching is O(W ) (also good). Additionally, since the destination trie is never visited again after finding the longest prefix, we can use any scheme we like for the top half of the trie. However... This scheme really only works in 2D: If, for example, our search terminates and finds that the port range specified for R5 doesn t match the packet, we have a serious problem.

37 Extended Grid-of-Tries (Baboescu et al. 2003) It is noted that in real-world classifiers, the number of rules that match a given packet for both source and destination address is very small: a linear search may not be terrible. The real problem with the Grid-of-tries is getting the complete list.

38 Extended Grid-of-Tries (Baboescu et al. 2003) It is noted that in real-world classifiers, the number of rules that match a given packet for both source and destination address is very small: a linear search may not be terrible. The real problem with the Grid-of-tries is getting the complete list. Solution: At each possible point of failure, add a jump pointer which allows the search to continue.

39 Extended Grid-of-Tries (Baboescu et al. 2003) R S D 1 00* 11* 2 01 * * 3 10* 00* 4 11* 00* * 6 * * 01* 8 010* 10* * f R5 f f

40 Extended Grid-of-Tries (Baboescu et al. 2003) Search: compose a list of all possible matching rules O(W 2 ) worst case...

41 Extended Grid-of-Tries (Baboescu et al. 2003) Search: compose a list of all possible matching rules O(W 2 ) worst case... however the worst case is strange and probably doesn t happen.

42 Extended Grid-of-Tries (Baboescu et al. 2003) Search: compose a list of all possible matching rules O(W 2 ) worst case... however the worst case is strange and probably doesn t happen. After searching, scan through the list and find the rule that best matches on the other fields.

43 Extended Grid-of-Tries (Baboescu et al. 2003) Search: compose a list of all possible matching rules O(W 2 ) worst case... however the worst case is strange and probably doesn t happen. After searching, scan through the list and find the rule that best matches on the other fields. Can apply path compression: N leaves 2N 1 nodes

44 Extended Grid-of-Tries (Baboescu et al. 2003) Search: compose a list of all possible matching rules O(W 2 ) worst case... however the worst case is strange and probably doesn t happen. After searching, scan through the list and find the rule that best matches on the other fields. Can apply path compression: N leaves 2N 1 nodes This works pretty well in practice, but can we do better?

45 Discussion/Questions???

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