There are three key points about making unstructured peer-to-peer networks more scalable: 1) The addition of supernodes, which are nodes with higher connectivity than typical nodes, can increase the capacity and scalability of unstructured P2P networks. 2) Graph theory provides theoretical bounds on searchability and diameter based on the number of nodes and maximum degree in a network. As the number of nodes increases, search time increases logarithmically. 3) Distributed hash tables implement a structured, decentralized P2P network with logarithmic diameter scaling and node degrees ranging from constant to logarithmic, providing better scalability than unstructured flooding networks.

1. Necessity of
Supernodes
David Hadaller, Kevin
Regan and Tyrel Russell

2. P2P Networks
Internet application
Application Layer Overlay Networks
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3. Problems of P2P Networks
Scalability
Security
Anonimity
Fault Tolerant
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4. P2P
Structured Unstructured
Networks
Centralized Napster ???
Decentralized Chord/Tapestry Gnutella/Kazaa
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5. The centralized and unstructured
decentralized systems are not scalable
in their vanilla form
Structured decentralized networks are
scalable
But require the topology to be of a
certain structure
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6. Alternatives...
The addition of supernodes seems to
make unstructured decentralized
networks scalable
Why?
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7. Three Directions
Traditional Decentralized
Unstructured (Flooding) P2P
Networks
Graph Theoretical Bounds
Decentralized Structured P2P
Networks
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8. What is a Peer-to-
Peer System?
Most commonly used for file sharing
Napster released 1999, shutdown 2001
Gnutella released 2000
Kazaa released 2001
Today: millions of users sharing
petabytes of data

9. System Interaction
User issues a keyword search
Network returns list of peers contain
matching files

10. Architecture
A peer operates as both a client and a
server
Idea: Everyone is equal, everyone
cooperates (both not true)
File sharing:
-FastTrack (Kazaa, Kazaa Lite)
-Gnutella (Morpheus, LimeWire)

11. How do Unstructured Peer-
to-Peer Systems Work?

12. Scalability Issues
Gnutella not
scalable

13. Making Gnutella Scalable
Chawathe et al. obtained 3 to 5x improvement in system capacity
Adding nodes of higher degree
Kazaa

14. Host Characteristics
6% users very well connected
10% of sessions >5 hrs

15. Impact of File Sharing
Study at the University of Washington
P2P accounts for 43% Internet traffic
Web accounts for 14%

16. Graph Theory
Formulate the problem as a Graph
Theory Problem
Let the P2P network be a graph G
where G is a set of vertices V and
there exists an edge between two
nodes u,v∈V when u is a neighbour of
v in the overlay network
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17. Some Definitions
Maximum Degree We denote ∆ as the maximum over
the degree of all vertices of a graph.
Minimum (u,v)-path We denote the minimum path
between two vertices u, v, u ≠ v, as d(u, v).
Diameter We define diameter D as the length of the max
d(u, v) for all u, v ∈ V
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18. Moore Bound
Upper bound on number of vertices in
a graph with max degree Δ and
diameter D
D
n ≤ 1 + ∆ 1 + (∆ − 1) + · · · + (∆ − 1)
∆(∆ − 1)D − 2
≤ = n0 (D, ∆)
∆−2
n(∆−2)+2
log ∆
D≥
log(∆ − 1)
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19. Moore Bound
d(u,v) = D
v
d(u,v) = 2 v
v
d(u,v) = 1
v v
!-1
v
v
!-1
v
u
!
v
v
n ≤ 1 + ∆ 1 + (∆ − 1) + · · · + (∆ − 1)D
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20. Special Graphs
Moore Graph
Have equivilence in the Moore bound
Diameter of 2: Moore graphs only exist with Δ = 3, 7, 57
Diameter more than 3: No Moore graphs exist
de Bruijn Graph
8 4
Leland-Solomon Graph 6 3
9 2
7 1
5 0
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21. Random Graphs
We are interested in property Q, so for a graph of size n
Enumerate the number of possible graphs with Q
If proportion of graphs with Q → 1 as n → ∞
Then we say that almost every graph has property Q
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22. Random Graphs
Some properties: almost every graph
has diameter 2
is k-connected for a fixed k > 2
has no complete subgraph Hk where k > 2log2n
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23. Random Graphs
For a fixed Δ ≥ 3 almost every Δ-regular graph has diameter
6∆
D ≥ log∆−1 n + log∆−1 logn − log∆−1 +1
∆−2
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24. Graph Theory
Summary
There is a theorectical limit to search in a
P2P network
As logn increases the time to search will
increase by roughly O(logn)
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25. Distributed Hash
Tables
Distributed Hash Tables (DHTs) are
an implementation of a decentralized,
structured peer-to-peer network
The diameter of the network scales
logarithmically with the size of the
network
Node degree varies from O(1) to
O(log n)
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26. Implementations
Tapestry - Plaxton Mesh
CAN - d-dimensional Torus
Pastry - Logical Ring
Chord - Logical Ring with Chords
Koorde - Logical Ring with deBruijn Graphs
HyperCuP - Hypercube
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27. Number of
Name Degree Diameter
Nodes
Tapestry N O(log N) O(log N)
CAN N O(d) O(n1/d)
Pastry N O(log N) O(log N)
Chord N O(log N) O(log N)
Koorde N O(1) O(log N)
HyperCuP N O((b-1)l) O(log N)

28. Conclusion
Graph theory gives us a way to bound
almost any random graph with a given
number of nodes and a maximum
degree
Flooding P2P networks have looked at
scalability from an empirical
perspective
Distributed Hash Tables provide a
scalable method for P2P at the cost of
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29. Questions?
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