Lossy Compression of Packet Classifiers Author: Ori Rottenstreich, Janos Tapolcai Publisher: 2015 IEEE International Conference on Communications Presenter:

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.

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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.

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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.

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Lossless compression

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Lossy compression

Lossy compression is a methodology for achieving higher compression ratios at the cost of losing some information about the represented object.

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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.

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Lossy compression

Approximate Classification Cached Classification

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Approximate Classification

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Cached Classification

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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.

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Optimization problems

The approximation ratio of a classifier ϕ (α,ϕ) =

Approximate classification

error ratio of ϕ = 1 − (α,ϕ) Cached classification

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Approximate Classification

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Cached Classification

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Greedy algorithm

The prefix rule popularity

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Greedy algorithm

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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.

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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

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Dynamic programming based algorithm

For a non-leaf node x and number of rules n ≥ 1, the function g(x,n,a) satisfies

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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.

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Dynamic programming based algorithm

Cached classification

The optimal approximation ratio satisfies

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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).

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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.

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Experimental results

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Experimental results

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Experimental results

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Experimental results

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Experimental results

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