Packet classification using diagonal-based tuple space search

1. Packet classification using diagonal-based tuple space search Authors:Fu-Yuan Lee *, Shiuhpyng Shieh Publish:Computer Networks 50 (2006) 1831–1842 Present:Chi-Lu Yang (楊淇祿) Date:October, 30, 2007 Department of Computer Science and Information Engineering National Cheng Kung University, Taiwan R.O.C.

2. Outline • 1. Introduction • Problem statement • 2. Fundamentals of tuple space • Fundamentals of the tuple space search (概述,同2001那一篇) • Proposed tuple space search strategy • 3. Diagonal-based tuple space schema • 3.1 Create Markers(Fig. and alg.) • 3.2 Create Conflict Resolvers—auxiliary filter(Fig. and alg.) • 3.3 Perform Pre-computation(Fig. and alg.) • 3.4 Find TImdton diagonal tuples • 4. Tuple space construction and search algorithm • 4.1 Construct Tuple Groups • 4.2 Binary search scheme • 4.3 Others discussion : Dynamic update of filter sets– Insert, Delete • 5. Performance evaluation and comparison • 6. Conclusions

3. Introduction • Filtersare grouped according to prefix lengths. • Tuple Space Framework searches on composition of prefix specifications. • The number oftuples is generally much smaller than the number offilters. • This approach will: • focus on reducing time for classification, • extend the tuple space framework to perform hash-based binary search on the tuple space.

4. Problem statement • A packet p is said to matcha filterf if and only if prefixes of the selected packet header fields of p are correspondingly the same as the prefixes specified by f. • It’s possible that a packet can match more than one filter. • Each filter is associated with a priority. The highest priority is selected as the best matched filter. • Packet classification is also the process of determining the best matched filter for the packet p.

5. Fundamentals of tuple space • Ta(i,j), S(Ta), L(Ta), IC(Ta) • L(Ta): leave markers • S(Ta): pre-compute best filter for F belong toTa(i,j)

6. Fundamentals of tuple space (cont.) • If no matched filter is found in a tuple T for a given packet, filters mapped to tuples in L(T) can be eliminated from the search space. (Fig.2) • If the probe in T returns a match, the search space can be restricted to the filters mapped to the tuples in L(T) and IC(T). ( Fig. 3)

7. Define Conflict (overlap) Resolved • Definition of Filter conflict resolved: • (1) For any pair of (fi, fj), fi ≠ fj, fi does not overlap with fj. • (2) For each pair of overlapped filters (fi, fj), fi ≠ fj, there must be a filter which is equivalent to the resolver of fi and fj. • Definition of Filter-Marker conflict resolved: • For any pair of filter and marker (fi,mj), if fi overlaps with mj then there must be a filter equivalent to the resolver of fj and mj. • where fi denotes a filter in F, and • mj represents a marker of a filter fj,

8. Proposed tuple space search strategy • Lemma 1: • Given a filter-marker conflict resolved tuple space, if there is a filter or marker in tuple T which can match a given packet p, then filters mapped to tuples in S(T) and IC(T) can be eliminated from the search space.

9. Diagonal-based tuple space schema

10. 3.1 Create Markers • A filter f mapped to tuple (i, j). Let s = min(i, j). Then markers of filter f are inserted into tuples from (i, j) to (s, s) and from (s, s) to (1, 1). • For example, as shown in Fig. 4, filters mapped to tuple (16, 24) leave markers in tuples (16, 23), (16, 22), (16, 21), . . . , (16, 17), (16, 16), (15, 15), . . . , (2, 2), (1, 1).

11. 3.2 Create Conflict Resolvers— auxiliary filters • Step1:Resolvers are created for each pair of overlapped filters in the original filter set F. • Step2:a resolver is created if there is a filter overlapp-ed with a marker in a diagonal tuple. • Filter f in tuple T(i, j): let i < j. Conflicts only need be examined between f and markers in diagonal tuples from (i+1, i+1) to (j-1, j-1). (Fig.5) • 更詳細完整請見p 1413--p1415, Fig.6. –Fig11.

12. 3.2 Create Conflict Resolvers (Cont.) — Alg. Create resolvers for F-M • 更詳細完整請見Alg.2. , p 1417左上角與p1418左上角。

13. 3.3 Perform Pre-computation • Pre-computation is performed for all the filters. (See Alg.4.) • including the filters in the original classifier F, markers and resolvers.

14. 3.4 Find TImdton diagonal tuples • As proved in Lemma 1: (Fig. 12.) • If a matched filter is found in a diagonal tuple, then Region 2 can be eliminated from the search space. • If no matched filter is found in a diagonal tuple, then there can’t be any matched filters in L(T). Region 1 can be eliminated from the search space.

15. 3.4 Find TImdton diagonal tuples (Cont.) • TImdt := T(m, m), last matched diagonal tuple : • (1) If there is a matched filter found in a diagonal tuple T(m, m), AND • (2) If there is no matched filter found in tuple T(m + 1, m + 1), • ===> • then the remaining search space can be restricted to tuples: {(i, j) | i = m, m <= j <= w or j = m, m<= j <= w}. • An example (Fig. 13.) : • If Tlmdt = (16, 16), then the remaining search space includes tuples: • (32, 16), (31, 16), (30, 16) . . . , (16, 16), (16, 17), . . . , (16, 31), (16, 32).

16. 3.4 Find TImdton diagonal tuples (Cont.) • Tlmdt is determined by: • (1) a naive search algorithm is to probe all remaining tuples and thus requires O(w) hashes. • (2) However, the search time can be further reduced by applying binary search on the remaining tuple. Thus, only O(log(w)) hash probes in total is required. • Our improvement is based on observation : All the remaining tuples are either in the same column or row with Tlmdt.

17. 4.1 Construct balanced binary search tree for tuple groups • TG(i) - Tuple groups: collection of non-empty tuples in the same column or row. • TG(i).col • TG(i).row

18. 4.2 Binary search scheme • The diagonal-based tuple space search algorithm: (Alg.5.) • (1) First, the algorithm performs binary search to determines Tlmdt using balanced binary search tree, diagonal-tuple tree. • (2) Next, the search algorithm traverses the row tree and column tree corresponding to the Tlmdt. • In this way, a best matched filter can be determined in O(log(w)) hash operation.

19. Performance evaluation

20. Conclusions • In this paper, authors proposed a algorithm for packet classification: • A binary search algorithm in O(log(w)) hash operations. • The memory usage can reach O(n2)in the worst case.