Lossy Compression of Packet Classifiers Author: Ori Rottenstreich, J’anos Tapolcai Publisher: 2015 IEEE International Conference on Communications Presenter: Yi-Hao Lai Date: 2015/12/09 Department of Computer Science and Information Engineering National Cheng Kung University, Taiwan R.O.C.
29
Embed
Lossy Compression of Packet Classifiers Author: Ori Rottenstreich, Janos Tapolcai Publisher: 2015 IEEE International Conference on Communications Presenter:
Introduction Measurement show that Internet traffic tends to follow the Zipf distribution and that a large portion of the traffic comes from a small number of flows. Accordingly traffic matches the classification rules in a biased distribution such that some of the classifier information is very seldom useful. National Cheng Kung University CSIE Computer & Internet Architecture Lab 3
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Lossy Compression of Packet Classifiers
Author: Ori Rottenstreich, J’anos TapolcaiPublisher: 2015 IEEE International Conference on Communications Presenter: Yi-Hao LaiDate: 2015/12/09
Department of Computer Science and Information Engineering National Cheng Kung University, Taiwan R.O.C.
Introduction
In recent years there has been a rapid growth in the size of classification and routing tables resulting in a scalability problem.
Compression has gained attention recently as a way to deal with the expected increase of classifier size while keeping it semantically-equivalent to its original form.
National Cheng Kung University CSIE Computer & Internet Architecture Lab
2
Introduction
Measurement show that Internet traffic tends to follow the Zipf distribution and that a large portion of the traffic comes from a small number of flows.
Accordingly traffic matches the classification rules in a biased distribution such that some of the classifier information is very seldom useful.
National Cheng Kung University CSIE Computer & Internet Architecture Lab
3
Lossless compression
Huffman coding and the Lempel-Ziv-Welch algorithm are well known lossless compression schemes. Lossless compression of packet classifiers has been deeply investigation in the last decades.
The ORTC algorithm achieves an optimal representation with a minimal number of prefix rules.
National Cheng Kung University CSIE Computer & Internet Architecture Lab
4
Lossless compression
National Cheng Kung University CSIE Computer & Internet Architecture Lab
5
Lossy compression
Lossy compression is a methodology for achieving higher compression ratios at the cost of losing some information about the represented object.
National Cheng Kung University CSIE Computer & Internet Architecture Lab
6
Lossy compression
In the main scheme of our approach, a unique action must be returned for all packets that cannot be classified due to the lossy representation of the classifier.
For the unclassified packets we can then calculate the classification in an alternative slower module.
National Cheng Kung University CSIE Computer & Internet Architecture Lab
7
Lossy compression
Approximate Classification Cached Classification
National Cheng Kung University CSIE Computer & Internet Architecture Lab
8
Approximate Classification
National Cheng Kung University CSIE Computer & Internet Architecture Lab
9
Cached Classification
National Cheng Kung University CSIE Computer & Internet Architecture Lab
10
Model and Notation
A prefix classifier = (→,…, →) For any packet header x , we have ∈ ϕ(x) = ,
where → is the rule with longest length that matches x.
A unique action ‘?’ A default action A∈ A header distribution P, where denotes the
probability of a header x.
National Cheng Kung University CSIE Computer & Internet Architecture Lab
11
Optimization problems
The approximation ratio of a classifier ϕ (α,ϕ) =
Approximate classification
error ratio of ϕ = 1 − (α,ϕ) Cached classification
National Cheng Kung University CSIE Computer & Internet Architecture Lab
12
Approximate Classification
National Cheng Kung University CSIE Computer & Internet Architecture Lab
13
Cached Classification
National Cheng Kung University CSIE Computer & Internet Architecture Lab
14
Greedy algorithm
The prefix rule popularity
National Cheng Kung University CSIE Computer & Internet Architecture Lab
15
Greedy algorithm
National Cheng Kung University CSIE Computer & Internet Architecture Lab
16
Dynamic programming based algorithm
Let r be the root of the complete binary tree of leaves that includes all headers. For a node x (represented by a corresponding prefix) in the complete binary tree, we consider an encoding with a maximal number of rules n satisfying ∈that its last rule (among the n) is of the form x → a for an action a A.∈
We define the function g(x,n,a) as the maximal ratio of headers from the subtree x that can be classified correctly by such an encoding.
National Cheng Kung University CSIE Computer & Internet Architecture Lab
17
Dynamic programming based algorithm
start by setting the values of g(x,n,a) for a leaf (header) x
Let y be a prefix that represents such a monochromatic subtree
National Cheng Kung University CSIE Computer & Internet Architecture Lab
18
Dynamic programming based algorithm
For a non-leaf node x and number of rules n ≥ 1, the function g(x,n,a) satisfies
National Cheng Kung University CSIE Computer & Internet Architecture Lab
19
Dynamic programming based algorithm
The optimal approximation ratio satisfies
The Approximate Classification problem can be optimally solved in O(W · · |A| · n2) time and O(W2 · ·|A|·n2) space, where is the number of rules in an exact encoding of the classifier.
National Cheng Kung University CSIE Computer & Internet Architecture Lab
20
Dynamic programming based algorithm
Cached classification
The optimal approximation ratio satisfies
National Cheng Kung University CSIE Computer & Internet Architecture Lab
21
More general classifiers
Unconstrained Dissimilarity a classifier with at most n rules that minimizes the dissimilarity ∆P(α, ).
One-Sided Dissimilarity a classifier with at most n rules that minimizes the dissimilarity ∆P(α,φ) while satisfying x ∀ ∈, (x) ≥ α(x).
National Cheng Kung University CSIE Computer & Internet Architecture Lab
22
Two-Dimensional Classifiers
For a prefix x in the first field and a prefix y in the second, we calculate an optimal encoding of the headers in the rectangle (x,y). Such a rectangle represents the Cartesian product of the two subtrees that correspond to the prefixes x, y in the two fields.
National Cheng Kung University CSIE Computer & Internet Architecture Lab
23
National Cheng Kung University CSIE Computer & Internet Architecture Lab
24
Experimental results
National Cheng Kung University CSIE Computer & Internet Architecture Lab
25
Experimental results
National Cheng Kung University CSIE Computer & Internet Architecture Lab
26
Experimental results
National Cheng Kung University CSIE Computer & Internet Architecture Lab
27
Experimental results
National Cheng Kung University CSIE Computer & Internet Architecture Lab
28
Experimental results
National Cheng Kung University CSIE Computer & Internet Architecture Lab