Search and Replication in Unstructured Peer-to-Peer Networks

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Search and Replication in Unstructured
Peer-to-Peer Networks

• Pei Cao
• Cisco Systems, Inc.
• (Joint work with Christine Lv, Edith Cohen, Kai
  Li and Scott Shenker)

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Disclaimer

• Results, statements, opinions in this talk do not
  represent Cisco in anyway
• This talk is about technical problems in
  networking, and does not discuss moral, legal and
  other issues related to P2P networks and their
  applications

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Outline

• Brief survey of P2P architectures
• Evaluation methodologies
• Search methods
• Replication strategies and analysis
• Simulation results

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Characteristics of Peer-to-Peer Networks

• Unregulated overlay network
• Current application file swapping
• Dynamic nodes join or leave frequently
• Example systems
• Napster, Gnutella
• Freenet, FreeHaven, MajoNation, Alpine, ...
• JXTA, Ohaha,
• Chord, CAN, Past, Tapestry, Oceanstore

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Architecture Comparisons

• Napster centralized
• A central website to hold file directory of all
  participants Very efficient
• Scales
• Problem Single point of failure
• Gnutella decentralized
• No central directory use flooding w/ TTL
• Very resilient against failure
• Problem Doesnt scale

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Architecture Comparisons

• Various research projects such as CAN
  decentralized, but structured
• CAN distributed hash table
• Structure all nodes participate in a precise
  scheme to maintain certain invariants
• Extra work when nodes join and leave
• Scales very well, but can be fragile

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Architecture Comparisons

• FreeNet decentralized, but semi-structured
• Intended for file storage
• Files are stored along a route biased by hints
• Queries for files follow a route biased by the
  same hints
• Scales very well
• Problem would it really work?
• Simulation says yes in most cases, but no proof
  so far

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Our Focus Gnutella-Style Systems

• Advantages of Gnutella
• Support more flexible queries
• Typically, precise name search is a small
  portion of all queries
• Simplicity, high resilience against node failures
• Problems of Gnutella Scalability
• Bottleneck interrupt rates on individual nodes
• Self-limiting network nodes have to exit to get
  real work done!

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Evaluation Methodologies

• Simulation based
• Network topology
• Distribution of object popularity
• Distribution of replication density of objects

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Evaluation Methods

• Network topologies
• Uniform Random Graph (Random)
• Average and median node degree is 4
• Power-Law Random Graph (PLRG)
• max node degree 1746, median 1, average 4.46
• Gnutella network snapshot (Gnutella)
• Oct 2000 snapshot
• max degree 136, median 2, average 5.5
• Two-dimensional grid (Grid)

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Modeling Methods

• Object popularity distribution pi
• Uniform
• Zipf-like
• Object replication density distribution ri
• Uniform
• Proportional ri ? pi
• Square-Root ri ? ? pi

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Evaluation Metrics

• Overhead average of messages per node per
  query
• Probability of search success Pr(success)
• Delay of hops till success

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Load on Individual Nodes

• Why is a node interrupted
• To process a query
• To route the query to other nodes
• To process duplicated queries sent to it

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Duplication in Flooding-Based Searches
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3
2
4
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5
7
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. . . . . . . . . . . .

• Duplication increases as TTL increases in
  flooding
• Worst case a node A is interrrupted by N q
  degree(A) messages

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Duplications in Various Network Topologies
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Relationship between TTL and Search Successes
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Problems with Simple TTL-Based Flooding

• Hard to choose TTL
• For objects that are widely present in the
  network, small TTLs suffice
• For objects that are rare in the network, large
  TTLs are necessary
• Number of query messages grow exponentially as
  TTL grows

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Idea 1 Adaptively Adjust TTL

• Expanding Ring
• Multiple floods start with TTL1 increment TTL
  by 2 each time until search succeeds
• Success varies by network topology
• For Random, 30- to 70- fold reduction in
  message traffic
• For Power-law and Gnutella graphs, only
• 3- to 9- fold reduction

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Limitations of Expanding Ring
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Idea 2 Random Walk

• Simple random walk
• takes too long to find anything!
• Multiple-walker random walk
• N agents after each walking T steps visits as
  many nodes as 1 agent walking NT steps
• When to terminate the search check back with the
  query originator once every C steps

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Search Traffic Comparison
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Search Delay Comparison
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Lessons Learnt about Search Methods

• Adaptive termination
• Minimize message duplication
• Small expansion in each step

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Flexible Replication

• In unstructured systems, search success is
  essentially about coverage visiting enough nodes
  to probabilistically find the object gt
  replication density matters
• Limited node storage gt whats the optimal
  replication density distribution?
• In Gnutella, only nodes who query an object store
  it gt ri ? pi
• What if we have different replication strategies?

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Optimal ri Distribution

• Goal minimize ?( pi/ ri ), where ? ri R
• Calculation
• introduce Lagrange multiplier ?, find ri and ?
  that minimize
• ?( pi/ ri ) ? (? ri - R)
• gt ? - pi/ ri2 0 for all i
• gt ri ? ? pi

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Square-Root Distribution

• General principle to minimize ?( pi/ ri ) under
  constraint ? ri R, make ri propotional to
  square root of pi
• Other application examples
• Bandwidth allocation to minimize expected
  download times
• Server load balancing to minimize expected
  request latency

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Achieving Square-Root Distribution

• Suggestions from some heuristics
• Store an object at a number of nodes that is
  proportional to the number of node visited in
  order to find the object
• Each node uses random replacement
• Two implementations
• Path replication store the object along the path
  of a successful walk
• Random replication store the object randomly
  among nodes visited by the agents

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Evaluation of Replication Methods

• Metrics
• Overall message traffic
• Search delay
• Dynamic simulation
• Assume Zipf-like object query probability
• 5 query/sec Poisson arrival
• Results are during 5000sec-9000sec

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Distribution of ri
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Total Search Message Comparison

• Observation path replication is slightly
  inferior to random replication

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Search Delay Comparison
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Summary

• Multi-walker random walk scales much better than
  flooding
• It wont scale as perfectly as structured
  network, but current unstructured network can be
  improved significantly
• Square-root replication distribution is desirable
  and can be achieved via path replication