LECTURE 3: ARCHITECTURES:

SUPPLEMENTARY SLIDES ON PLAXTON

ROUTING

CA4006 Lecture Notes (Martin Crane 2015) 1Lecture 3: Architectures: Supplementary on Plaxton

Plaxton Routing• Plaxton, Rajamaran and Richa: mechanism for efficient

dissemination of objects in a network, published in 1997

– Before P2P systems came about!

• Basic idea: prefix-oriented routing (assume fixed no. of nodes)

– Store object ID=A at node with ID of longest common prefix with A

• If many such nodes exist, choose node with longest common suffix

– Goal: uniform data dissemination

– Routing based on pointer list (object – node mapping) and

neigbour list (primary + secondary neighbours)

• Basis for well-known DHTs Pastry, etc (and follow-up projects)

– Method adapted to needs of P2P systems + simplified

CA4006 Lecture Notes (Martin Crane 2015) 2Lecture 3: Architectures: Supplementary on Plaxton

0…

01..010. 011.

012. 013.0131

0110

0112

03..030. 031.

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02..

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00..

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000. 001.

003.

Pastry Example

3CA4006 Lecture Notes (Martin Crane 2015)Lecture 3: Architectures: Supplementary on Plaxton

1…

10.. 11..

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122.

120. 121.

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130. 131.

132. 133.

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Pastry: Topology• Identifier space:

– 2�-bit identifiers (typically: � = 128), wrap-around at 2�− 1 ↔ 0

– Interpret identifiers to the base of 2� (typically: � = 4, base 16)

– Prefix-based tree topology

– Leaves: keys & node IDs; (key, value) pairs under numerically

closest node

managed by

xxx

l=6: 6-bit identifiersb=2: base 4

0xx 1xx 2xx 3xx

00x 01x 02x 03x 10x 11x 12x 13x 20x 21x 22x 23x 30x 31x 32x 33x

key node

4Lecture 3: Architectures: Supplementary on Plaxton © Prof Michael Welzl

Pastry: Routing Basics• Example

• Goal: find node responsible for �, e.g. 120

• Tree-based search for lookup(�)

– Traverse tree search structure top-down

• Prefix-based routing for lookup(�)

– Approximate tree search in distributed scenario

– Forward query to known node with longest prefix matching �

xxx

0xx 1xx 2xx 3xx

00x 01x 02x 03x 10x 11x 12x 13x 20x 21x 22x 23x 30x 31x 32x 33x

5Lecture 3: Architectures: Supplementary on Plaxton © Prof Michael Welzl

Pastry: Routing Basics (/2)

• Routing in Pastry:

– Each step, route towards “numerically“

closest node

• That is, query is routed to a node with a

one character longer prefix (= b Bits)

� � log�� � routing steps

– If that is not possible:

• Route towards node numerically closer to ��

012321

321321

022222

013331

012110

012300

012322

012321

Destination:

Start

1. Hop

2. Hop

3. Hop

4. Hop

5. Hop

Destination:

(b = 2)

6Lecture 3: Architectures: Supplementary on Plaxton © Prof Michael Welzl

xxx

0xx 1xx 2xx 3xx

00x 01x 02x 03x 10x 11x 12x 13x 20x 21x 22x 23x 30x 31x 32x 33x

?xx: 011 1 - 301

1?x: 102 - 2 -

12?: 0 - - 123

Pastry: Routing Table• Routing table

– Long distance links to other prefix realms

– �/� rows: one per prefix length

– 2� − 1 columns: 1 per digit different from local node ID

– Routing table for node 120: