ad-hoc limited scale-free models for unstructured peer-to-peer networks

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1 IEEE P2P, Aachen, Germany, September 2008 Ad-hoc Limited Scale-Free Models for Unstructured Peer- to-Peer Networks Hasan Guclu ([email protected] ) Los Alamos National Laboratory Durgesh Kumari ([email protected] ) Murat Yuksel ([email protected] ) University of Nevada – Reno

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Ad-hoc Limited Scale-Free Models for Unstructured Peer-to-Peer Networks. Hasan Guclu ( [email protected] ) Los Alamos National Laboratory Durgesh Kumari ( [email protected] ) Murat Yuksel ( [email protected] ) University of Nevada – Reno. Outline. Motivation - PowerPoint PPT Presentation

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Page 1: Ad-hoc Limited Scale-Free Models for Unstructured Peer-to-Peer Networks

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IEEE P2P, Aachen, Germany, September 2008

Ad-hoc Limited Scale-Free Models for Unstructured Peer-to-Peer Networks

Hasan Guclu ([email protected])Los Alamos National Laboratory

Durgesh Kumari ([email protected])

Murat Yuksel ([email protected])University of Nevada – Reno

Page 2: Ad-hoc Limited Scale-Free Models for Unstructured Peer-to-Peer Networks

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Outline

Motivation Topology Generation Mechanisms

Barabási-Albert (Preferential Attachment) Model Our Model with Local Info, Hard Cutoffs, and Churn

Search Methods Flooding Normalized Flooding Random Walk

Summary and Conclusions

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Motivation: Scale-Free Topologies

Characterization is free of the system size N (i.e.,

scale).

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Motivation

Diameterd

Exponent

Number of stubsm

O(lnln N) (2,3) ≥1

O(ln N/lnln N) 3 ≥2

O(ln N) 3 1

O(ln N) >3 ≥1

Search Efficiency vs. Exponent and Connectedness

Ultra-small

Small-world

Characteristics of the p2p overlay topology has significant effects on the search performance.

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Motivation

Key Question: How to construct the overlay topology by using local information in p2p nets such that the search efficiency is good?

Scale-freeness (i.e. power-law exponent) is related to search efficiency

Key Constraints: No global knowledge No peer wants to take on the load – hard cutoff on the

degree

Local decisions affecting global behavior: When a new peer joins, how should it construct its list of

neighbors? When a new peer leaves, how should its neighbors rewire

themselves to the network?

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IEEE P2P, Aachen, Germany, September 2008

6Topology Generation Model: Preferential Attachment w/ Hard Cutoff

How to construct a scale-free topology? Preferential Attachment (PA)

Include an existing peer with probability proportional to its current degree.

prefer the peers with larger degree Requires global info

? Hmmm.

Which node to have as a neighbor?

Degrees7433222111

26

Prob. of Attachment

0.270.150.120.120.080.080.080.040.040.04

1

We revise PA such that a node with maximum allowed degree (i.e., hard cutoff) is skipped. And the procedure is tried again..

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IEEE P2P, Aachen, Germany, September 2008

Topology Generation Model: Parameters

Parameters of our topology construction framework

Probability of a node going

down/leaving.Horizon of available state information at

join.Horizon of available state information at

leave.

Maximum degree a node is allowed to

have.

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IEEE P2P, Aachen, Germany, September 2008

Topology Generation Model: Join w/ j

Join() procedure: Select a node J to start

with Collect J’s neighborhood

topology information within j hops

Apply PA on the j sub-topology until m links are established

If m is larger than the nodes in the subtopology, repeat the procedure again until m links are established.

Hmmm. Which m nodes to have as a neighbor?

J

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Topology Generation Model: Rewiring w/ l after a Leave

Leave() procedure: Select a node L to delete Collect L’s neighborhood

topology information within l hops

Let the l sub-topology information be available to L’s 1-hop neighbors, r1 and r2

With L’s information and r1 or r2 being removed

r1 and r2 apply PA on their l sub-topology until the lost link is restored with another peer

L

r2

r1

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IEEE P2P, Aachen, Germany, September 2008

Topology Generation Model: Growth with Joins and Leaves

Topology growth process calls Join() or Leave() procedures depending on the amount of churn.

At every iteration: Call Join() Call Leave() with a probability

Keep this iteration going until the target network size is reached

Both the Join() and Leave() procedures assure that degrees of nodes are less than the hard cutoff

Higher means more churn.

A peer is added at every iteration.

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IEEE P2P, Aachen, Germany, September 2008

Degree Distributions, =0m=1, kc=50 m=1, no cutoff

Increase in j shifts degree distribution from Exponential to

scale-free.

Increase in j shifts degree distribution from Exponential to

scale-free.

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IEEE P2P, Aachen, Germany, September 2008

Degree Distributions, =0

m=3, kc=50 m=3, no cutoff

Lesson: Force peers to have a larger m to reduce the need for large j.

Larger m makes the shift less apparent.

Larger m makes the shift less apparent.

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Degree Distributions, =0.3m=1, kc=50 m=1, no cutoff

Hard cutoff does not affect this

distribution shift..

Contribution of l in shifting the degree distribution is more

significant.

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Search Methods

Flooding Source node sends a message to all its neighbors and

every node which receives the message forwards it to all its neighbors except the node the message is received from until the target node receives the message

Normalized flooding Similar to flooding but the nodes send the messages to

at most m (minimum number of links in the network) neighbors

Random walk The nodes send the messages only to one of their

neighbors except the source node

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Flooding, =0, m=3

Cutoff is the main factor defining flooding search

performance.

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Flooding: =0.1, 0.3; m=3=0.3, kc=10=0.1, kc=10

Lesson: Use churn as an opportunity to restructure the network topology by carefully rewiring the peers.

Churn with larger l helps flooding performance!!

Churn with larger l helps flooding performance!!

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Normalized Flooding: m=3j=2, l=1j=2, l=0

Again, larger l reduces the negative effect of churn!!

Again, larger l reduces the negative effect of churn.Performance of Random Walk exhibit a similar behavior to Normalized

Flooding.Lesson: State information at leave is more valuable

than the one at join.

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Design Guidelines & Principles

Force all peers to have a larger m (i.e., a minimum of 3) to reduce the need for large j.

Information at the time of leave is more valuable than the information at the time of join

A little responsible leave results in significantly better search performance for the leftover network

Rewiring is helpful – Churn can be used as an opportunity to restructure the network

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Summary & Future Work

A generic topology growth model with churn local state info hard cutoffs rewiring

Scales larger than N=10,000

Models looking at dynamic behavior are worthy of pursuing..

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Thank you!

THE END

AcknowledgmentsThis work was supported by the U.S. Department of Energy under contract DE-AC52-

06NA25396 and by the US National Science Foundation under awards 0627039 and 0721542.