ALGORITHMS FOR PERFORMANCE AND TRUST IN PEERTOPEER SYSTEMS

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ALGORITHMS FOR PERFORMANCE AND TRUST IN
PEER-TO-PEER SYSTEMS
Hui Zhang University of Southern California
2
Outline

• Introduction to Peer-to-Peer (P2P) systems three
  layers in system design.
• Algorithms for performance on the overlay routing
  layer.
• Algorithms for performance on the underlying
  network layer.
• Algorithms for trust at the application layer.
• Conclusion future work.

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P2P Networked systems

• A collaborating group of Internet end-hosts which
  overlay their own special-purpose network atop
  the Internet.
• Examples
• file sharing Napster,Gnutella - anonymous
  publishing Freenet
• distributed storage Dabek2001,Kubiatowicz2000,IV
  Y,PAST
• web caching Iyer2002 - DoS attack
  preventionKeromytis2002
• application-layer multicast Castro2003,Ratnasamy
  2001,Zhuang2001
• naming Cox2002,Balakrishnan2004 - event
  notificationScribe
• indirection services Stoica2002, etc.

4
Challenges in P2P system design

• Allow rapid deployment through self organization
• Scale with increasing network size
• Adapt to dynamics from both the underlying
  network and the application layer.

5
Three layers in a P2P system design
Application layer
Overlay routing layer
Underlying network layer
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Algorithmic issues in P2P system design

• Overlay routing layer
• Distributed hash table algorithms.
• Underlying network layer
• Exploiting network proximity and Internet
  topology.
• Application layer
• Distributed and robust rating algorithms.

7
Outline

• Introduction to Peer-to-Peer (P2P) systems three
  layers in system design.
• Algorithms for performance on the overlay routing
  layer.
• Algorithms for performance on the underlying
  network layer.
• Algorithms for trust at the application layer.
• Conclusion future works.

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Distributed Hash Tables

• Support a hash table-like functionality on
  Internet-like scale
• A global key space each data item is a key in
  the space, and each node is responsible for a
  portion of the key space.
• Given a key, map it onto a node.
• Examples Freenet Clarke et al. 2001,
  CANRatnasamy et al. 2001, Chord Stoica et al.
  2001, PastryRowstron et al. 2001,
  TapestryZhao et al. 2001, KademliaMaymounkov
  et al. 2002, ViceroyMalkhi et al. 2002,
  KoordeKaashoek et al. 2003, etc.

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Small-world model Kleinberg1999

• Small-world graphs have
• short-distance clustering (like regular graph)
• long-distance shortcuts (result in short global
  path length like random graph)
• How to find short paths in a distributed fashion?
  

Local contact
log2(N) average routing path length
Shortcut
Probability 1/j
i
ij
An one-dimensional small-world network example
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Small-world Freenet

• Files are identified by binary file keys obtained
  by applying a hash function.
• Each node maintains a datastore and a routing
  table of ltkey,pointergt values.
• Greedy forwarding search with backtracking.
• Enhanced-clustering cache replacement
• Each node chooses a seed randomly when joining
  the network
• When a new key (file) u is to be cached, the node
  chooses in the current datastore the key v
  farthest from the seed
• If Distance (u, seed) lt Distance (v, seed), cache
  u and evict v with probability 1-P (clustering)
• If Distance (u, seed) gt Distance (v, seed), cache
  u and evict v with probability P (randomness).

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Small-world Freenet - analysis

• The expected steps to deliver a message in the
  idealized small-world Freenet is O(log N) if the
  routing table size is ?(log2 N), where N is the
  network size.

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Small-world Freenet routing structure

• When i has log(N) shortcuts, its routing table
  resembles that of a Chord node in a probabilistic
  way!

i
i1
iN
iN/4
iN/2
Node is shortcut distribution on the distance
space
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Outline

• Introduction to Peer-to-Peer (P2P) systems three
  layers in system design.
• Algorithms for performance on the overlay routing
  layer.
• Algorithms for performance on the underlying
  network layer.
• Algorithms for trust at the application layer.
• Conclusion future works.

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Frugal routing

• A Distributed Hash Table routing scheme is frugal
  if
• The search space for the key decreases by a
  constant factor after each lookup hop
• The next hop after each intermediate node x in
  the route depends only on x and the destination.
• Examples small-world Freenet, Chord, Pastry,
  Tapestry.
• Latency stretch Ratnasamy et al. 2001

The lookup latency on the overlay topology
between two nodes

The unicast latency on the underlying topology
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Latency stretch vs. latency expansion

• Theorem 1
• If the underlying topology G is drawn from
  a family of graphs with exponential latency
  expansion, then the expected latency stretch of
  any frugal routing scheme is ?(logN), where N is
  the network size.

• Theorem 2
• If
• (1) the underlying topology G is drawn from a
  family of graphs with d-power-law latency
  expansion, and
• (2) for each node u in a frugal routing network,
  it samples (log N)d nodes in each range with
  uniform randomness and keeps the pointer to the
  nearest node for future routing,
• then the expected latency stretch of a
  request is O(1).

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Lookup-Parasitic Random Sampling
1. Recursive lookup. 2. Each intermediate hop
appends its IP address to the lookup message.
3. When the lookup reaches its target, the
target informs each listed hop of its
identity. 4. Each intermediate hop then sends one
(or a small number) of pings to get a reasonable
estimate of the latency to the target, and update
its routing table accordingly. 5. When the target
key is random to the initial node, a sample on
each range (of some node) happens with the same
probability 1/2.
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Internet latency expansion

• The performance of many other networking
  algorithms relies on the latency expansion
  characteristic of the underlying network.
• Request latency reduction in web cache systems
  Plaxton et al. 1997 .
• Nearest neighbor search Karger et al. 2002 .
• Locality-aware DHT design Abraham et al. 2004 .
• Gossip-based communication mechanisms Kempe et
  al. 2002.
• The Internet router-level topology has an
  exponential expansion Phillips et al. 1999.
• The expansion is defined on router-level hops
• How about the expansion in terms of latency?

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Internet latency expansion measurement
methodology

• Collected two router-level topologies.
• - one in May 2002 with 328378 routers, and the
  other in November 2003 with 356648 routers.
• Randomly sampled about 100,000 node pairs from
  each topology and used their latency to estimate
  Internet latency expansion.
• Approximated link latency between any two nodes
  by the accumulated geographic distance of the
  path between the two nodes in shortest path
  routing.
• - assign geo-locations to nodes using the
  Geotrack tool.

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Internet router-level topology latency expansion

• The hop-count expansion of the Internet
  router-level topology is exponential
• The latency expansion of the Internet
  router-level topology is power-law and has an
  exponent between 1 and 2.

Internet latency expansion (in log-log)
Comparison of the two topologies (in log-log)
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Latency expansion at the city level

• Nu(x) ? Cu(x)
• Nu(x) the latency expansion function defined
  on routers.
• Cu(x) the latency expansion function defined
  on cities.

The Internet link topology has low expansion rate
after being embedded into the two-dimensional
geographical sphere.
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Outline

• Introduction to Peer-to-Peer (P2P) systems three
  layers in system design.
• Algorithms for performance on the overlay routing
  layer.
• Algorithms for performance on the underlying
  network layer.
• Algorithms for trust at the application layer.
• Conclusion future works.

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Autonomous peers and selfish behaviors

• Peers have many options to control their own
  participation in an open P2P system.
• Resource configuration parameters, file
  re-sharing decision, on-off switch, .
• Peers are prone to show selfish behaviors when
  there is no incentive to cooperate.
• Free-riding phenomenon Adar et al. 2000Saroiu
  et al. 2001.
• Most files (e.g., 98 reported in Adar et al.
  2000) belong to a small percentage of the users
  (20\, respectively).
• A majority of the users are one-time,
  one-hour'' users.

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Building social trust in P2P users

• Reputation systems Okita2003
• A means of describing social trust networks.
• A rating system is used to produce a consensus
  about the merit of any given member.
• Effective at
• Incentivizing user cooperation.
• Isolating malicious users.
• Adjudging node reliability,
• On-line examples
• Livejournal, Friendster, eBay, Advogato.

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Eigenvector-based reputation systems

• A referential link structure
• Nodes represent entities (users, merchants,
  authors of blogs.)
• Links represent endorsement of one user by
  another.
• Eigenvector or stationary distribution based
  rating schemes.
• HIST Kleinberg1999, PageRank Brin et al.
  1998, etc.

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PageRank Brin1998

• A rating scheme to rank hypertext documents on
  the WWW.
• An iterative algorithm to calculate the
  importance of a web page based on the importance
  of its parent pages.
• Can be applied to other systems than WWW.

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PageRank random walk model
node
referential link
The walker
X
1/2
1/3
Z
Y

• As time goes on, the expected percentage of steps
  the walker is at each node v converges to the
  PageRank weight PR(v).

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P2P rating schemes

• Design issues
• distributed rating
• collusion-proof rating

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A supervisorbased distributed implementation of
PageRank

• In a supervisory directed graph
• Each user v has a designated supervisor to
  calculate PR(v).
• Any user is random to its supervisors.
• No small supervising loop exists.
• There is a fast reactive approach for any user j
  to deliver a message to any other user is
  supervisors, and the path never includes i.

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A Chord supervising overlay
Network user
Supervising Pointer
A Chord network with 8 users and 8-bit key space
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PageRank is it collusion-proof?

• Can a node easily boost its rank by manipulating
  its out-going (endorsing) links with others?

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Amp(G) a metric on group collusion
WG(G) PR(i)PR(j)
Win(G)
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Answer for (11 ?) in PageRank

• In the original PageRank system,
• where ? is the resetting probability.

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Two experimental topologies

• W, a Web link topology
• Contains the link structure of upwards of 80
  million URLs.
• Source the Stanford WebBase.
• B, a weblog blogrolling topology
• Contains the blogrolling structure of upwards of
  72,000 blogs.
• Source www.blogstreet.com, the XML-RPC webblog
  service.

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Experiment Collusion200

• Model a small number of web pages simultaneously
  colluding.
• Methodology
• 100 colluding groups
• Each colluding group has the circle topology
  consisting of two nodes with adjacent ranks
• Arbitrarily chose nodes originally ranked around
  1000th, 2000th, , 100000th.
• ? 0.15.

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Experiment result of Collusion200 (I)
W - Amplification factors of the 100
colluding groups in Collusion200.
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Experiment result of Collusion200 (III)
W new PR rank after Collusion200.
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There is a long flat portion
The PR weight distribution of 4 topologies.
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Next step how to detect collusions?

• Theorem on group detection hardness.
• Max G?G Amp(G) is a NP-Hard
  problem.

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An observation on collusion behaviors

• To increase their PR weight, i.e., the stationary
  weight in the random walk, the colluding nodes
  will stall the random walk.

• When the resetting probability ? increases, the
  colluding nodes must suffer a significant drop in
  PR weight.
• Therefore, we expect the PR weight of colluding
  nodes to be highly correlated with 1/ ? (the
  average walk length), while that of non-colluding
  nodes is relatively insensitive to the change in
  ?.

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Adaptive-resetting scheme

• Part I collusion detection
• Given the topology, calculate the PR vector under
  different ? values.
• ? 0.0375, 0.05, 0.075, 0.15, 0.3, 0.45,
  0.6, ?default 0.15.
• Calculate the correlation coefficient between the
  curve of each node x's PR weight and the curve of
  1/ ?. Label it as co-co(x).

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Experiment result of Collusion200 (IV)
W - Amplification factors of the 100
colluding groups in Collusion200.
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Experiment result of Collusion200 (VI)
W new PR rank after Collusion200.
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Topology analysis on W and B
a small loop of two top nodes in W
a star-like sub-graph in B
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Dropped out
New top-25 URL list in W
Dropping
New
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Conclusion

• A set of algorithms for performance and trust in
  P2P systems.
• Their technical merits were well acknowledged.
• They have or will been implemented in real
  applications.
• Small-world Freenet source code implemented and
  tested in Freenet.
• LPRS-Chord in grid computing Min et al. 2004.
• Collusion-robust reputation systems for Weblog
  community.

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Future work

• Building dynamic virtual communities with P2P
  techniques.
• An unified information management infrastructure
  to accommodate and connect diverse virtual
  communities.
• Web study from algorithmic perspective.
• Web ranking
• Web community detection.

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Publications

• Improving Eigenvector-based Reputation Systems
  Against Collusion. With Ashish Goel, Ramesh
  Govindan, Kahn Mason, and Benjamin Van Roy.
  Invited for Special issue of Journal of Internet
  Mathematics for WAW04, under review.
• Improving Lookup Latency in Distributed Hash
  Table Systems using Random Sampling. With Ashish
  Goel and Ramesh Govindan. To appear in ACM/IEEE
  Transactions on Networking.
• An Empirical Evaluation of Internet Latency
  Expansion. With Ashish Goel and Ramesh Govindan.
  To appear in ACM SIGCOMM Computer Communication
  Review.
• Using the Small-World Model to Improve Freenet
  Performance. With Ashish Goel and Ramesh
  Govindan. Computer Networks Journal. Volume 46,
  Issue 4, Page 555-574, November 2004.
• Advanced Query Techniques for Wide-Area Network
  Monitoring . With Xin Li, Fang Bian, Christophe
  Diot, Ramesh Govindan, Wei Hong, and Gianluca
  Iannacoone. The first IEEE International Workshop
  on Networking Meets Databases, 2005.
• Fast, Memory-Efficient Traffic Estimation by
  Coincidence Counting . With Fang Hao,
  Muralidharan S. Kodialam, T. V. Lakshman. IEEE
  INFOCOM 2005.
• Making Eigenvector-based Reputation Systems
  Robust to Collusion . With Ashish Goel, Ramesh
  Govindan, Kahn Mason, and Benjamin Van Roy. The
  third Workshop on Algorithms and Models for the
  Web Graph, October 2004.
• The Design of A Distributed Rating Scheme for
  Peer-to-peer Systems . With Debojyoti Dutta,
  Ashish Goel and Ramesh Govindan. The first
  Workshop on Economic Issues in Peer-to-Peer
  Systems, Berkeley, CA (June 5-6, 2003).
• Incrementally Improving Lookup Latency in
  Distributed Hash Table Systems . With Ashish Goel
  and Ramesh Govindan. appeared in ACM SIGMETRICS,
  2003.
• Using the Small-World Model to Improve Freenet
  Performance. With Ashish Goel and Ramesh
  Govindan. appeared in IEEE INFOCOM, 2002.

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Thanks!
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backup
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In a Freenet node
Node x
datastore
routing table
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In a Freenet node
Node x
datastore
routing table
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In a Freenet node
Node x
datastore
routing table
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In a Freenet node
Node x
datastore
routing table
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In a Freenet node
Node x
datastore
routing table
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In a Freenet node
Node x
datastore
routing table
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In a Freenet node
Node x
datastore
routing table
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In a Freenet node
Node x
datastore
routing table
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In a Freenet node
Node x
datastore
routing table
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In a Freenet node
Node x
datastore
routing table
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In a Freenet node
request for file 70
Node x
datastore
routing table
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In a Freenet node
request for file 70
Node x
datastore
routing table
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In a Freenet node
Node B
request for file 70
Node x
datastore
routing table
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Latency stretch in frugal routing
latency for each lookup on the overlay topology

average latency on the underlying topology

• In frugal routing, ?(logN) hops per lookup in
  average
• ?(logN) stretch with no optimization.
• Could it be done better, e.g., O(1) stretch,
  without much change?

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Term definition Latency expansion

• Let Nu(x) denote the number of nodes in the
  network G that are within latency x of node u.
• - Power-law latency expansion Nu(x) grows (i.e.
  expands') proportionally to xd, for all nodes
  u.
• Examples ring (d1), mesh (d2).
• - Exponential latency expansion Nu(x)
  grows proportionally to ?x for some constant ? gt
  1.
• Examples random graphs.

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LPRS-Chord topology with power-law expansion
Ring Stretch
(at time 2logN)
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LPRS-Chord convergence time
Convergence Time
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LPRS-Chord on Internet subgraphs
Stretch on the router-level graph (at time 2logN)