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.
1
Outline
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1. Introduction
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Problem statement
2. Fundamentals of tuple space
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Fundamentals of the tuple space search (概述,同2001那一篇)
Proposed tuple space search strategy
3. Diagonal-based tuple space schema
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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 TImdt on diagonal tuples
4. Tuple space construction and search algorithm
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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
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Introduction
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Filters are grouped according to prefix lengths.
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Tuple Space Framework searches on
composition of prefix specifications.
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The number of tuples is generally much
smaller than the number of filters.
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This approach will:
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focus on reducing time for classification,
extend the tuple space framework to perform hashbased binary search on the tuple space.
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Problem statement
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A packet p is said to match a filter f if and only if
prefixes of the selected packet header fields of p are
correspondingly the same as the prefixes specified by f.
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It’s possible that a packet can match more than one
filter.
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Each filter is associated with a priority. The highest
priority is selected as the best matched filter.
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Packet classification is also the process of determining
the best matched filter for the packet p.
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Fundamentals of tuple space
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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)
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Fundamentals of tuple space (cont.)
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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)
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Define Conflict (overlap) Resolved
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Definition of Filter conflict resolved:
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(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:
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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,
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Proposed tuple space search strategy
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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.
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Diagonal-based tuple space schema
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3.1 Create Markers
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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).
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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).
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3.2 Create Conflict Resolvers
— auxiliary filters
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Step1:Resolvers are
created for each pair of
overlapped filters in the
original filter set F.
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Step2:a resolver is created
if there is a filter overlapped 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)
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更詳細完整請見p 1413-p1415, Fig.6. –Fig11.
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3.2 Create Conflict Resolvers (Cont.)
— Alg. Create resolvers for F-M
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更詳細完整請
見Alg.2. , p
1417左上角與
p1418左上角。
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3.3 Perform Pre-computation
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Pre-computation is
performed for all the
filters. (See Alg.4.)
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including the filters in the
original classifier F,
markers and resolvers.
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3.4 Find TImdt on diagonal tuples
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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.
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3.4 Find TImdt on diagonal tuples (Cont.)
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TImdt := T(m, m), last matched
diagonal tuple :
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(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.) :
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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).
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3.4 Find TImdt on diagonal tuples (Cont.)
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Tlmdt is determined by:
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(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.
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4.1 Construct balanced binary
search tree for tuple groups
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TG(i) - Tuple groups: collection of nonempty tuples in the same column or row.
• TG(i).col
• TG(i).row
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4.2 Binary search scheme
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The diagonal-based tuple space search
algorithm: (Alg.5.)
• (1) First, the algorithm performs binary search
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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.
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Performance evaluation
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Conclusions
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In this paper, authors proposed a algorithm for
packet classification:
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A binary search algorithm in O(log(w)) hash
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operations.
The memory usage can reach O(n2) in the
worst case.
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