Locality Aware Network Solutions

Dahlia MalkhiThe Hebrew University of Jerusalem

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A Brief Overview of Distributed Computing

The 90’s: – Internet activity: Web browsing

– Paradigm: Client-server

– Techniques: cluster computing, Paxos, group communication

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A Brief Overview of Distributed Computing

The 90’s: 2000-

– Internet activity: File sharing

– Paradigm: P2P, grid, web-services

– Techniques: overlay networks, content distribution networks, resource location

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Application: IPv6 Routing over IPv4[van Renesse 02]

AF3S:::3FF1:43E4

0001:::3BBB:5555

1111:::7777:7754

2222:::2222:2222

EEE0:::EEEE:EEEE

5151:::6161:6666

567A:::0202:0202

8888:::0909:9999

Distribute Hash Tables (DHT)

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Application: Content Delivery / Finding Nearest Copies of Data

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?

?

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Application: Hyperencryption[Maurer 92, Ding & Rabin 02]

Random bits

Alice BobKey

Adversary bits

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Application: A Hyperencryption P2P Network

[Rabin 03]Distributed Hash Table

(DHT)

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Application: A Distributed Google?

?

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ever-growing global scale-free networks, their provisioning, repair and unique functions

EVERGROW

The Vision

ultimate RAID

ultimate GNUTELLA

ultimate GOOGLE

ultimate AKAMAI

infrastructure and new methods and systems devoted to measurement, mock-up and and analysis of present and future network traffic, topology and logical structure, to bridge the gap in theory, protocols and understanding to what the Internet can be in 2025.

An EC project. Coordinators: SICS (Sweden) and HUJI (Jerusalem)

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Scalable Network Solutions

Overlay networks provide added functionality at the application level– Search, routing, location services

Network theory provides the foundations– Possibilities, impossibilities, lower/upper bounds

Practical solutions require flexible deployment

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Distributed Data Structures (DDS)

Peers jointly implement a data structure, e.g., hash table

Route queries based on data-name (key)

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DDS Problem Reduced to Routing?? 00001111

Responsible for 00001111

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Why classic routing network designs don’t help

Static # of nodes a priori

known Node labels

designated by network designer

000

111

110

101001

100

011

010

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DDS Reduced to Routing

The problem: Overlay routing network– Variants: labeled routing,

name-independent routing, finding nearest copies

Dynamic emulation

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Distributed Hash Tables

[Malkhi, Naor, Ratacjzak, PODC 2002]

SchemeDegreeRoute

Chord, Tapestry, Pastry [2001]

Log nLog n

CAN [2001]

dd*n(1/d)

Viceroy [2002]

5Log n

Koorde, D2B, DH, generic

[2003]

2Log n

[Abraham, Awerbuch, Azar, Bartal, Malkhi, Pavlov, IPDPS 2003]

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Tree View of Dynamic Graphs

Leafs of the tree represent current nodes

Inner nodes in the tree represent nodes that were split

000

111

110

101

00

110 111

001

100

011

010

000 001 010 011 100 101

00

Example: merge of 000, 001 into 00

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Locality awareness

source

target

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Locality awareness

source

target

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Locality Awareness in Overlay Networks

Model the network as a weighted undirected graph– c(x, y): cost of shortest path from x to y– c() is a metric

An overlay network is a sub-graph Let x=x0 , x1, …, xt=y be a route in the overlay

network Stretch: Ratio between overlay route cost and

shortest path cost:( c(x, x1) + c(x1,x2) + … c(xt-1, y) ) / c(x,y)

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Overlay Networks inGrowth-Bounded Metrics

Previous work:– [Plaxton, Rajaraman, Rica 1997], Tapestry (Berkeley),

Pastry (MS UK)

– Expected (large) constant stretch– Logarithmic node degree

LAND [Abraham, Malkhi, Dobzinski, SODA 2004]:– Guaranteed stretch (1+ε)– Expected logarithmic node degree, constant

depends on growth-bound– Simple, intuitive construction and proofs

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Overlay Networks in Geometric Spaces

Modeling the Internet as a geometric space is practical– Ubiquitous GPS devices– Successful embeddings in virtual

coordinate-space Problem 1: Locate nodes Problem 2: Route to known coordinates

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Location Services and Routingin Geometric Spaces

LLS: First fully-locality aware location service [Abraham Dolev Malkhi 2004]

– bounded stretch lookup– bounded stretch update

First constant-degree routing scheme (to known coordinates)[Abraham Malkhi, PODC 2004]

– constant node degree, logarithmic hops, 1+ε stretch

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Routing in Arbitrary Graphs: Lower and upper bounds

Name-independent routing: node names are independent of routing scheme [Awerbuch, Bar Noy, Linial, Peleg 1989]

Lower bounds: [Gavoille Gengler 2001] – Stretch < 3 O(n) routing information– Stretch < 5 √n routing information

Upper bound: [Abraham, Gavoille, Malkhi, Nisan, Thorup, SPAA 2004]

– stretch-3 routing with O(√n ) routing information– Stretch 3 is indeed attainable!

General upper bound: [Abraham Gavoille, Malkhi, DISC 2004]

– Stretch-k routing with memory O(k2 k√n )

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Network nodes

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Nodes’ random identifiers

0111010

0011110 1111110

0001000

10010010101001

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Coloring and Vicinities

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Coloring and Vicinities

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?

?

?

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Stretch 3

?

d

≤ d

≤ 2d

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The Full Routing Scheme

?

12

345

?a

b

c

d

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Locality-Aware, Robust Overlay for

Information Lookup and Content Delivery Degree O(√n) Locality awareness:

– Formally stretch 3– For far-apart nodes, lower stretch

Mostly two-hop– Whenever full connectivity exists

Flexibility – Estimate √n roughly– Cache information on many vicinity nodes– Store information about any known node of same color

Fault tolerance:– Multiple route choices– Quick repair– Maintain QoS in face of churn

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