scale-free overlay topologies with hard cutoffs for unstructured peer-to-peer networks
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Scale-Free Overlay Topologies with Hard Cutoffs for Unstructured Peer-to-Peer Networks. Murat Yuksel University of Nevada – Reno [email protected]. Hasan Guclu Los Alamos National Laboratory [email protected]. Outline. Motivation and Problem Statement Topology Generation Mechanisms - PowerPoint PPT PresentationTRANSCRIPT
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
Murat YukselUniversity of Nevada – Reno
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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).
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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
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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
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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
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PA with Hard Cutoff
At steady state:
Total rate:Probability to connect to the nodes with degree k
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PA with Hard Cutoff
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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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