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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
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IEEE P2P, Aachen, Germany, September 2008
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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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IEEE P2P, Aachen, Germany, September 2008
Motivation: Scale-Free Topologies
Characterization is free of the system size N (i.e.,
scale).
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IEEE P2P, Aachen, Germany, September 2008
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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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IEEE P2P, Aachen, Germany, September 2008
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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
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Prob. of Attachment
0.270.150.120.120.080.080.080.040.040.04
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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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IEEE P2P, Aachen, Germany, September 2008
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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IEEE P2P, Aachen, Germany, September 2008
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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IEEE P2P, Aachen, Germany, September 2008
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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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IEEE P2P, Aachen, Germany, September 2008
Flooding, =0, m=3
Cutoff is the main factor defining flooding search
performance.
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IEEE P2P, Aachen, Germany, September 2008
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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IEEE P2P, Aachen, Germany, September 2008
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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IEEE P2P, Aachen, Germany, September 2008
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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IEEE P2P, Aachen, Germany, September 2008
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..