Scale-Free Overlay Topologies with Hard Cutoffs for Unstructured Peer-to-Peer Networks

IEEE ICDCS, Toronto, Canada, June 2007 (LA-UR-06-8032)

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Scale-Free Overlay Topologies with Hard Cutoffs for Unstructured Peer-

to-Peer Networks

Hasan GucluLos Alamos National

[email protected]

Murat YukselUniversity of Nevada – Reno

[email protected]

mailto:[email protected]




IEEE ICDCS, Toronto, Canada, June 2007

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Outline Motivation and Problem Statement Topology Generation Mechanisms

Barabási-Albert (Preferential Attachment) Model Configuration Model Hop-and-Attempt Preferential Attachment Discover-and-Attempt Preferential Attachment

Search Methods Flooding Normalized Flooding Random Walk

Summary and Conclusions


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Motivation

Diameterd

Exponent

Number of stubsm

O(lnln N) (2,3) ≥1O(ln N/lnln N) 3 ≥2

O(ln N) 3 1O(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

When a new peer joins, how should it construct its list of neighbors?

A local decision affecting global behavior (emergence).


Fat-tailed power-law degree distribution: No typical scale Two well-known topology generation algorithms:

Preferential Attachment (PA) by Barabasi and Albert.

Dynamic model (fixed exponent)

Configuration Model (CM) Static model Pre-defined degree distribution with a

parameterized exponent

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Scale-Free Topologies


Definition of natural cutoff:

For scale-free networks with power-law degree distribution (m: minimum degree)

Natural cutoff

Natural cutoff for PA model ( )

Hard cutoff is the value of the maximum degree imposed on nodes.

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Natural and Hard Cutoff


Preferential attachment (Barabási-Albert, PA) model (PA)

Configuration model (CM) Hop-and-attempt PA model (HAPA) Discover-and-attempt PA model

(DAPA)

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Network Generation Mechanisms


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Preferential Attachment (PA) Connect to an existing peer with

probability proportional to its current degree.

prefer the peers with larger degree simply skip the existing peers already

saturated their hard cutoffs Requires global info


PA with Hard Cutoff

At steady state:

Total rate:Probability to connect to the nodes with degree k


PA with Hard Cutoff


PA with Hard Cutoff


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Configuration Model (CM) Given a target hard cutoff and a power-law exponent,

generate the perfect scale-free degree distribution… allows multiple links and self loops may have disconnected components not practical, but does generate the best possible

scale-freeness within the hard cutoff constraint – i.e., good for studying


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Hop-and-attempt PA Model (HAPA)

At every time step a new node is added to the network This new node attempts to connect to a randomly chosen

existing node A by using the preferential attachment rule Then it attempts to connect to a randomly chosen node B

which is a neighbor of A The node repeats this procedure until it fills all its stubs (or

the number of links it has reaches m)


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Discover-and-attempt PA Model (DAPA)

First, a substrate network with a specific topology and a large number of nodes (we use geometric random network) is generated

A finite number of nodes are selected randomly and put into p2p network which is empty at the beginning

A node is randomly selected from the substrate network and let it send a broadcasting message to its neighbors reachable in sub steps

The selected node finds all the nodes in its horizon belonging to the peers network and attempts to connect by using the preferential attachment rule until having m links if possible

If it is connected to at least one peer it is added to the peers network

This process is repeated until the number of peers reaches to the number desired


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Discover-and-attempt PA Model (DAPA)


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Procedure

Global Information

PA YesCM YesHAPA PartialDAPA No

Global versus Local Information


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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 Similar to flooding but the nodes send the messages

only to one of their neighbors except the source node


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FloodingPA is better due to nodes at the edge


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Flooding

HAPA rocks, DAPA not bad


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Normalized Flooding

PA likes cutoff, CM does not.


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Normalized Flooding

The lower the cutoff the better the performance


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Normalized Flooding

Cutoff is goooood. Not so short-sighted network gives good results.


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Random Walk (The same number of messages in NF and RW)

PA likes cutoff, CM does not.


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Random Walk

The lower the cutoff the better the performance


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Random Walk

The lower the cutoff the better the performance.


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Conclusions In flooding the lower the hard cutoff the lower the

number of hits. HAPA without cutoff does especially good in flooding due to the star-like topology. Increasing the minimum degree eliminates the negative effect of the hard cutoff.

There exists an interplay between connectedness (m) and the degree distribution exponent if there is a hard cutoff, except CM.

Harder cutoffs may improve search efficiency in normalized flooding and random walk except CM.

Extended version of the paper in http://arxiv.org/abs/cs/0611128

Acknowledgments DOE (DE-AC52-06NA25396), NSF (0627039) and Sid

Redner (Boston University).


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Thank you!

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Scale-Free Overlay Topologies with Hard Cutoffs for Unstructured Peer-to-Peer Networks