layered interval codes for tcam-based classification
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Layered Interval Codes for TCAM-based Classification. Author: Anat Bremler-Barr, David Hay, Danny Hendler Publisher: IEEE INFOCOM 2009 Presenter: Chun-Yi Li Date: 2009/03/04. Introduction. - PowerPoint PPT PresentationTRANSCRIPT
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Layered Interval Codes for TCAM-based Classification
Author: Anat Bremler-Barr, David Hay, Danny Hendler
Publisher: IEEE INFOCOM 2009
Presenter: Chun-Yi Li
Date: 2009/03/04
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Introduction Range expansion was found to cause an increase of
more than 16% in TCAM space requirements for real-word databases.
The algorithms we present split the ranges between multiple layers, each of which consists of mutually disjoint ranges.
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IntroductionEncoding Example
Liu’s basic dependent encoding
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IntroductionEncoding Example
LIC encoding
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Outline
The Layered Interval Encoding Scheme Terminology The Layering Stage The Bits Allocation Stage The Encoding Stage
Performance
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The Layered Interval Encoding Scheme
Terminology Minimum-space LIC (MLIC)
The MLIC problem is to find a legal coloring C of G that minimizes
The MLIC problem is to output a LIC code for the ranges of S that uses a minimum number of bits.
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The Layered Interval Encoding Scheme
Terminology Minimum-space LIC (MLIC)
R4
R1
R2 R3R1
R2 R3
R4
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The Layered Interval Encoding Scheme
Terminology Budgeted minimum LIC (BMLIC)
An instance of BMLIC consists of a set S of weighted ranges and a positive integer b, the number of available bits.
Under this restriction, it is required to output a LIC code for a maximum-weight subset S’ of S.
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The Layered Interval Encoding Scheme
Terminology
weight – interval r’s total redundancy.Ex: R1 source port = [1,3] => 0001, 001*
destination port = [9,12] => 1001, 101*, 1100
total redundancy = 2*3-1=5
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The Layered Interval Encoding Scheme
The Layering Stage
Maximum Size Independent Sets (MSIS)This is a greedy layering algorithm that works iteratively. The algorithm finds a maximum size independent set.
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The Layered Interval Encoding Scheme
The Layering Stage
Maximum Size Colorable Sets (MSCS)An i-colorable set of a graph G is a subset of G’s vertices that can be colored with i colors. MSCS finds a maximum size i-colorable set of G.
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The Layered Interval Encoding Scheme
The Layering Stage Maximum Size Colorable Sets (MSCS)
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The Layered Interval Encoding Scheme
The Layering Stage
Maximum Weight Independent Sets (MWIS)Same as MSIS, except that we iteratively find a maximum weighted independent set.
Maximum Weight Colorable Sets (MWCS)Same as MSCS, except that, instead of finding maximum size k-colorable sets ,MWCS finds maximum weight k-colorable sets.
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The Layered Interval Encoding Scheme
The Bits Allocation Stage
Compute the above quantity for each layer Li, and assign the next bit to a layer for which this quantity is maximal.
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The Layered Interval Encoding Scheme
The Bits Allocation Stage
Sort Li’s interval in decreasing weight order
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The Layered Interval Encoding Scheme
The Encoding Stagek1 = assigned[m]
k2= assigned[m]
code[i][j] = *k1． bin(j)． *k2
‥‥ ‥‥ ‥‥‥‥ ‥‥ ‥‥ ‥‥‥‥‥ ‥‥
k1 bits
layer 1 layer 2 layer i layer i+1
k2 bits
b bits
layer n
assigned[i] is the number of bits assigner to i’th layer
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Outline
The Layered Interval Encoding Scheme Terminology The Layering Stage The Bits Allocation Stage The Encoding Stage
Performance
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Performance
Expansion and redundancy factors, using 36 extra bits, for different range encoding algorithms.
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Performance
The number of bits required to encode all the ranges that occur in our database as a function of the encoding scheme employed.
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Performance
Redundancy factor as a function of the number of extra bits for different encoding schemes.
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Performance
Redundancy factor as a function of the number of extra bits for different layering algorithms.