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An Efficient IP Address Lookup Scheme Using Balanced Binary Search with Minimal Entry and

Optimal Prefix Vector

Author: Hyuntae PARK, Hyejeong HONG and Sungho KANG Publisher: IEICE TRANS. COMMUN. 2011 Presenter: Li-Hsien, HsuData: 12/28/2011

Introduction

We propose an efficient binary search algorithm for IP address lookup in the Internet routers.

We propose a perfectly balanced search algorithm based on the binary search tree.

To preform the binary search properly, the BST algorithm strictly restricts that the enclosure prefix is stored in a higher level than its enclosed prefix so that the enclosure is compared earlier, and this restriction makes the binary search tree highly unbalanced in case that are many levels of prefix nesting.

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Introduction

3

P2P1

P3 P4

P0

P8

P9

P7

P5 P6

To construct a balanced binary search tree, we remove the prefix nesting relationship of nodes in the binary search tree and make each node hold a prefix vector containing the nesting information.

Definition: Leaf prefixes of the binary trie.

Ex ： P0, P1, P2, P5, P6, P7 or P9

P0

Introduction

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P2P1

P3 P4

P8

P9

P7

P5 P6

What is the prefix vector?Ex：

The prefix vector of P1 is [Y3, ø, ø, Y1, ø]

The prefix vector of P2 is [Y3, ø, ø, Y2, ø]

The prefix vector of P5 is [Y4, Y8, ø, ø, Y5]

The prefix vector of P6 is [Y4, Y8, ø, ø, Y6]

The prefix vector of P7 is [Y4, Y8, ø, Y7, ø]

P0

Introduction

5

P1

P3 P4

P8

P9

P7

P5 P6

What is the prefix vector?Ex：

The prefix vector of P1 is [Y3, ø, ø, Y1, ø]

The prefix vector of P2 is [Y3, ø, ø, Y2, ø]

The prefix vector of P5 is [Y4, Y8, ø, ø, Y5]

The prefix vector of P6 is [Y4, Y8, ø, ø, Y6]

The prefix vector of P7 is [Y4, Y8, ø, Y7, ø]

P0

Definition(1/3)

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P1

P3 P4

P8

P9

P7

P5 P6

S(Px,j) : sub-string of the most significant j bits of prefix Px.

L(Px): length of prefix Px.

V(Px):the prefix vector of Px

V(Px): the k-th vector element in V(Px)

P0

Definition(2/3)

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P1

P3 P4

P8

P9

P7

P5 P6

S(Px,j) : sub-string of the most significant j bits of prefix Px.

L(Px): length of prefix Px.

V(Px):the prefix vector of Px

V(Px): the k-th vector element in V(Px)

P0

Definition(3/3)

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P1

P3 P4

P8

P9

P7

P5 P6

S(Px,j) : sub-string of the most significant j bits of prefix Px.

L(Px): length of prefix Px.

V(Px):the prefix vector of Px

V(Px): the k-th vector element in V(Px)

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P2P1

P3 P4

P0

P8

P9

P7

P5 P6

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P2P1

P3 P4

P0

P8

P9

P7

P5 P6

P4

P8

P5P7

P3

P6 P9

PM1

gray node: ordinary or iso-likeness prefixes.

black node: likeness prefixes.

Search(1/5)

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Incoming address: 11001 best matching prefix length: 0 corresponding output port of the BMP: default

Search(2/5)

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Incoming address: 11001 best matching prefix length: 0 corresponding output port of the BMP: default

Search(3/5)

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Incoming address: 11001 best matching prefix length: 2 corresponding output port of the BMP: Y8

Search(4/5)

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Incoming address: 11001 best matching prefix length: 2 corresponding output port of the BMP: Y8

Search(5/5)

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Incoming address: 11001 best matching prefix length: 4 corresponding output port of the BMP: Y6

Performance Evaluation

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The number of entries in each scheme

Ne

The average numbers of memory accesses

Tav

The maximum numbers of memory accesses

Tmx

The required memory size M