Self-Stabilization in Tree-Structured P2P Service Discovery Systems - - PowerPoint PPT Presentation

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Self-Stabilization in Tree-Structured P2P Service Discovery Systems - - PowerPoint PPT Presentation

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Self-Stabilization in Tree-Structured P2P Service Discovery Systems edric Tedeschi 1 C Eddy Caron 2 , Ajoy K. Datta 3 , and Franck Petit 4 (1) INRIA Sophia Antipolis M editerran ee (2) LIP Lab., University of Lyon CNRS ENS Lyon

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SLIDE 1

Self-Stabilization in Tree-Structured P2P Service Discovery Systems

C´ edric Tedeschi1 Eddy Caron2, Ajoy K. Datta3, and Franck Petit4

(1) INRIA Sophia Antipolis M´ editerran´ ee (2) LIP Lab., University of Lyon — CNRS — ENS Lyon — UCB Lyon — INRIA (3) University of Nevada Las Vegas (4) MIS Lab., University of Picardie Jules Verne

Workshop APRETAF

  • Jan. 22nd
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SLIDE 2

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Context

Computing Needs

Cosmology Climate prediction Genomics Nuclear security

Computing Power Computational Grids

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 2/22

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SLIDE 3

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Context

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 2/22

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SLIDE 4

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Context

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 2/22

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SLIDE 5

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Context

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 2/22

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SLIDE 6

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Context

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 2/22

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SLIDE 7

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Context

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 2/22

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SLIDE 8

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Context

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 2/22

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SLIDE 9

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Context

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 2/22

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SLIDE 10

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Context

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 2/22

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SLIDE 11

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Context

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 2/22

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SLIDE 12

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Context

  • Service discovery in GRID Computing
  • Services (binary file, library) installed on servers
  • Servers declare their services, client discovers them
  • Target platforms: Peer-to-Peer Platform
  • Decentralized algorithms (no central infrastructure)
  • Distributed data structure for service retrieval
  • Large scale systems
  • Dynamic (joins and leaves of nodes)
  • Fault-tolerance

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 2/22

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SLIDE 13

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Context

  • Service discovery in GRID Computing
  • Services (binary file, library) installed on servers
  • Servers declare their services, client discovers them
  • Target platforms: Peer-to-Peer Platform
  • Decentralized algorithms (no central infrastructure)
  • Distributed data structure for service retrieval
  • Large scale systems
  • Dynamic (joins and leaves of nodes)
  • Fault-tolerance

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 2/22

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SLIDE 14

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Context

  • Service discovery in GRID Computing
  • Services (binary file, library) installed on servers
  • Servers declare their services, client discovers them
  • Target platforms: Peer-to-Peer Platform
  • Decentralized algorithms (no central infrastructure)
  • Distributed data structure for service retrieval
  • Large scale systems
  • Dynamic (joins and leaves of nodes)
  • Fault-tolerance

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 2/22

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SLIDE 15

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Different Approaches

1 Unstructured (Gnutella)

  • Flooding:

2 Structured

  • Distributed Hashing Table (DHT)
  • Routing
  • Full Search
  • Scalability (logarithmic state and path)
  • Tries (or Prefix Trees)

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 3/22

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SLIDE 16

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Different Approaches

1 Unstructured (Gnutella)

  • Flooding: Costly and Partial Search

2 Structured

  • Distributed Hashing Table (DHT)
  • Routing
  • Full Search
  • Scalability (logarithmic state and path)
  • Tries (or Prefix Trees)

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 3/22

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SLIDE 17

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Different Approaches

1 Unstructured (Gnutella)

  • Flooding: Costly and Partial Search

2 Structured

  • Distributed Hashing Table (DHT)
  • Routing
  • Full Search
  • Scalability (logarithmic state and path)
  • Tries (or Prefix Trees)

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 3/22

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SLIDE 18

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Different Approaches

1 Unstructured (Gnutella)

  • Flooding: Costly and Partial Search

2 Structured

  • Distributed Hashing Table (DHT) Exact Queries Only
  • Routing
  • Full Search
  • Scalability (logarithmic state and path)
  • Tries (or Prefix Trees)

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 3/22

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SLIDE 19

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Different Approaches

1 Unstructured (Gnutella)

  • Flooding: Costly and Partial Search

2 Structured

  • Distributed Hashing Table (DHT) Exact Queries Only
  • Routing
  • Full Search
  • Scalability (logarithmic state and path)
  • Tries (or Prefix Trees)

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 3/22

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SLIDE 20

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Trie-based Overlays

  • Advantages
  • Efficient range queries
  • Automatic completion of partial strings
  • Easy extension to multi-dimensional queries
  • Related Works
  • Skip Graphs (Aspnes and Shah – 2003)
  • P-Grid (Datta, Hauswirth, John, Schmidt, Aberer – 2003)
  • PHT (Ramabhadran, Ratnasamy, Hellerstein, Shenker – 2004)
  • Nodewiz (Basu, Banerjee, Sharma, Lee – 2005)
  • DLP-Tables (Caron, Desprez, Tedeschi – 2005)
  • Fault-tolerance: either ignored or based on replication
  • Replication: Costly. What can be done if k is reached?
  • Does not recover after arbitrary failures

(e.g., memory corruption)

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 4/22

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SLIDE 21

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Trie-based Overlays

  • Advantages
  • Efficient range queries
  • Automatic completion of partial strings
  • Easy extension to multi-dimensional queries
  • Related Works
  • Skip Graphs (Aspnes and Shah – 2003)
  • P-Grid (Datta, Hauswirth, John, Schmidt, Aberer – 2003)
  • PHT (Ramabhadran, Ratnasamy, Hellerstein, Shenker – 2004)
  • Nodewiz (Basu, Banerjee, Sharma, Lee – 2005)
  • DLP-Tables (Caron, Desprez, Tedeschi – 2005)
  • Fault-tolerance: either ignored or based on replication
  • Replication: Costly. What can be done if k is reached?
  • Does not recover after arbitrary failures

(e.g., memory corruption)

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 4/22

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SLIDE 22

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Trie-based Overlays

  • Advantages
  • Efficient range queries
  • Automatic completion of partial strings
  • Easy extension to multi-dimensional queries
  • Related Works
  • Skip Graphs (Aspnes and Shah – 2003)
  • P-Grid (Datta, Hauswirth, John, Schmidt, Aberer – 2003)
  • PHT (Ramabhadran, Ratnasamy, Hellerstein, Shenker – 2004)
  • Nodewiz (Basu, Banerjee, Sharma, Lee – 2005)
  • DLP-Tables (Caron, Desprez, Tedeschi – 2005)
  • Fault-tolerance: either ignored or based on replication
  • Replication: Costly. What can be done if k is reached?
  • Does not recover after arbitrary failures

(e.g., memory corruption)

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 4/22

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SLIDE 23

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Trie-based Overlays

  • Advantages
  • Efficient range queries
  • Automatic completion of partial strings
  • Easy extension to multi-dimensional queries
  • Related Works
  • Skip Graphs (Aspnes and Shah – 2003)
  • P-Grid (Datta, Hauswirth, John, Schmidt, Aberer – 2003)
  • PHT (Ramabhadran, Ratnasamy, Hellerstein, Shenker – 2004)
  • Nodewiz (Basu, Banerjee, Sharma, Lee – 2005)
  • DLP-Tables (Caron, Desprez, Tedeschi – 2005)
  • Fault-tolerance: either ignored or based on replication
  • Replication: Costly. What can be done if k is reached?
  • Does not recover after arbitrary failures

(e.g., memory corruption)

Best-Effort → Self-Stabilization

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 4/22

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SLIDE 24

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Self-Stabilization

  • General technique to tolerate transient faults
  • Guaranteed to converge to the intended behavior

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 5/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Self-Stabilizing Overlays for Peer-to-Peer Networks

  • Self-Stabilizing Tree (Herault et al. – 2007)
  • Self-Stabilizing Hypertree (Dolev and Kat – 2007)
  • Snap-Stabilizing Tries (Caron et al. – 2006)
  • Assumes a rooted connected tree
  • Written in a coarse grain communication model

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 6/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Self-Stabilizing Overlays for Peer-to-Peer Networks

  • Self-Stabilizing Tree (Herault et al. – 2007)
  • Self-Stabilizing Hypertree (Dolev and Kat – 2007)
  • Snap-Stabilizing Tries (Caron et al. – 2006)
  • Assumes a rooted connected tree
  • Written in a coarse grain communication model

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 6/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Contributions

Self-Stabilizing Trie Maintenance

  • Built in the P2P model
  • Message-Passing
  • Arbitrary initial topology
  • Comprehensive proof of stabilization
  • Simulation results

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 7/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Outline

1

P2P Network

2

Proper Greatest Common Prefix Tree

3

Self-Stabilizing PGCP Tree

4

Conclusion

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 8/22

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SLIDE 29

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Outline

1

P2P Network

2

Proper Greatest Common Prefix Tree

3

Self-Stabilizing PGCP Tree

4

Conclusion

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 9/22

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SLIDE 30

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

P2P Network

Physical Network Basic entity: peer (processor)

  • Message-Passing
  • P1 can communicate with P2 if

and only if P1 “knows” P2.

  • Runs logical nodes

Logical Tree Basic entity: (tree) node

  • Executes the protocol
  • Distributed among peers

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 10/22

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SLIDE 31

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

P2P Network

Physical Network Basic entity: peer (processor)

  • Message-Passing
  • P1 can communicate with P2 if

and only if P1 “knows” P2.

  • Runs logical nodes

Logical Tree Basic entity: (tree) node

  • Executes the protocol
  • Distributed among peers

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 10/22

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SLIDE 32

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Outline

1

P2P Network

2

Proper Greatest Common Prefix Tree

3

Self-Stabilizing PGCP Tree

4

Conclusion

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 11/22

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SLIDE 33

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Proper Greatest Common Prefix Tree (PGCP Tree)

Distributed Logical Structure

  • Dynamically constructed
  • Bounded degree and height

Definition Each node is the Proper Greatest Com- mon Prefix of any pair of its children

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 12/22

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SLIDE 34

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Proper Greatest Common Prefix Tree (PGCP Tree)

Distributed Logical Structure

  • Dynamically constructed
  • Bounded degree and height

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 12/22

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SLIDE 35

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Proper Greatest Common Prefix Tree (PGCP Tree)

Distributed Logical Structure

  • Dynamically constructed
  • Bounded degree and height

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 12/22

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SLIDE 36

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Proper Greatest Common Prefix Tree (PGCP Tree)

Distributed Logical Structure

  • Dynamically constructed
  • Bounded degree and height

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 12/22

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SLIDE 37

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Proper Greatest Common Prefix Tree (PGCP Tree)

Distributed Logical Structure

  • Dynamically constructed
  • Bounded degree and height

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 12/22

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SLIDE 38

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Proper Greatest Common Prefix Tree (PGCP Tree)

Distributed Logical Structure

  • Dynamically constructed
  • Bounded degree and height

Lookup

  • Exact match
  • Autocompletion
  • Range queries

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 12/22

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SLIDE 39

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Proper Greatest Common Prefix Tree (PGCP Tree)

Distributed Logical Structure

  • Dynamically constructed
  • Bounded degree and height

Lookup

  • Exact match
  • Autocompletion
  • Range queries

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 12/22

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SLIDE 40

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Proper Greatest Common Prefix Tree (PGCP Tree)

Distributed Logical Structure

  • Dynamically constructed
  • Bounded degree and height

Lookup

  • Exact match
  • Autocompletion
  • Range queries

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 12/22

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SLIDE 41

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Arbitrary Initial Configuration

Expected PGCP Tree

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 13/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Arbitrary Initial Configuration

An Arbitrary Labeled Tree

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 13/22

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SLIDE 43

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Arbitrary Initial Configuration

An Arbitrary Labeled Forest

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 13/22

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SLIDE 44

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Outline

1

P2P Network

2

Proper Greatest Common Prefix Tree

3

Self-Stabilizing PGCP Tree

4

Conclusion

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 14/22

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SLIDE 45

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

Infinite Cycle (Timeout)

1 Parent processing

  • Bad Prefix Relation
  • Reduction of root number
  • Creation of roots

2 Children processing

  • Merge
  • Prefix Relation
  • GCP

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 15/22

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SLIDE 46

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

Infinite Cycle (Timeout)

1 Parent processing

  • Bad Prefix Relation
  • Reduction of root number
  • Creation of roots

2 Children processing

  • Merge
  • Prefix Relation
  • GCP

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 15/22

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SLIDE 47

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

Infinite Cycle (Timeout)

1 Parent processing

  • Bad Prefix Relation
  • Reduction of root number
  • Creation of roots

2 Children processing

  • Merge
  • Prefix Relation
  • GCP

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 15/22

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SLIDE 48

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

Infinite Cycle (Timeout)

1 Parent processing

  • Bad Prefix Relation
  • Reduction of root number
  • Creation of roots

2 Children processing

  • Merge
  • Prefix Relation
  • GCP

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 15/22

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SLIDE 49

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

Infinite Cycle (Timeout)

1 Parent processing

  • Bad Prefix Relation
  • Reduction of root number
  • Creation of roots

2 Children processing

  • Merge
  • Prefix Relation
  • GCP

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 15/22

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SLIDE 50

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

Infinite Cycle (Timeout)

1 Parent processing

  • Bad Prefix Relation
  • Reduction of root number
  • Creation of roots

2 Children processing

  • Merge
  • Prefix Relation
  • GCP

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 15/22

slide-51
SLIDE 51

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

Infinite Cycle (Timeout)

1 Parent processing

  • Bad Prefix Relation
  • Reduction of root number
  • Creation of roots

2 Children processing

  • Merge
  • Prefix Relation
  • GCP

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 15/22

slide-52
SLIDE 52

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

Infinite Cycle (Timeout)

1 Parent processing

  • Bad Prefix Relation
  • Reduction of root number
  • Creation of roots

2 Children processing

  • Merge
  • Prefix Relation
  • GCP

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 15/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Protocol

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 16/22

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P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Sketch of proof

1 Stabilized communications

(Awerbuch et al. 1996)

2 Only present processes 3 Parent’s copies of

child labels are correct

4 Prefix relations are correct 5 Number of roots = 1 6 The tree satisfies the PGCP

tree definition

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 17/22

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SLIDE 74

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Sketch of proof

1 Stabilized communications

(Awerbuch et al. 1996)

2 Only present processes 3 Parent’s copies of

child labels are correct

4 Prefix relations are correct 5 Number of roots = 1 6 The tree satisfies the PGCP

tree definition

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 17/22

slide-75
SLIDE 75

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Sketch of proof

1 Stabilized communications

(Awerbuch et al. 1996)

2 Only present processes 3 Parent’s copies of

child labels are correct

4 Prefix relations are correct 5 Number of roots = 1 6 The tree satisfies the PGCP

tree definition

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 17/22

slide-76
SLIDE 76

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Sketch of proof

1 Stabilized communications

(Awerbuch et al. 1996)

2 Only present processes 3 Parent’s copies of

child labels are correct

4 Prefix relations are correct 5 Number of roots = 1 6 The tree satisfies the PGCP

tree definition

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 17/22

slide-77
SLIDE 77

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Sketch of proof

1 Stabilized communications

(Awerbuch et al. 1996)

2 Only present processes 3 Parent’s copies of

child labels are correct

4 Prefix relations are correct 5 Number of roots = 1 6 The tree satisfies the PGCP

tree definition

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 17/22

slide-78
SLIDE 78

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Sketch of proof

1 Stabilized communications

(Awerbuch et al. 1996)

2 Only present processes 3 Parent’s copies of

child labels are correct

4 Prefix relations are correct 5 Number of roots = 1 6 The tree satisfies the PGCP

tree definition

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 17/22

slide-79
SLIDE 79

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Sketch of proof

1 Stabilized communications

(Awerbuch et al. 1996)

2 Only present processes 3 Parent’s copies of

child labels are correct

4 Prefix relations are correct 5 Number of roots = 1 6 The tree satisfies the PGCP

tree definition

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 17/22

slide-80
SLIDE 80

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Simulation: Convergence Time

10 20 30 40 50 60 70 80 500 1000 1500 2000 Convergence Time Graph size 5 trees 10 trees 20 trees 30 trees 50 trees 75 trees 100 trees

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 18/22

slide-81
SLIDE 81

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Simulation: Convergence Time

20 40 60 80 100 500 1000 1500 2000 2500 3000 Convergence time Graph size [avg]

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 18/22

slide-82
SLIDE 82

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Simulation: Communication Amount

5 10 15 20 25 30 500 1000 1500 2000 Number of messages (per node, per time step) Graph size 5 trees 10 trees 20 trees 30 trees 50 trees 75 trees 100 trees

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 19/22

slide-83
SLIDE 83

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Simulation: Communication Amount

2 4 6 8 10 12 14 16 18 200 400 600 800 1000 1200 1400 Communications (per node, per time step) Graph size [avg]

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 19/22

slide-84
SLIDE 84

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Simulation: Performance

0.2 0.4 0.6 0.8 1 10 20 30 40 50 Satisfaction ratio Time 2 failures 4 failures 8 failures 16 failures 32 failures

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 20/22

slide-85
SLIDE 85

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Outline

1

P2P Network

2

Proper Greatest Common Prefix Tree

3

Self-Stabilizing PGCP Tree

4

Conclusion

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 21/22

slide-86
SLIDE 86

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Conclusion

  • Contributions
  • Practical P2P prefix tree maintenance
  • Comprehensive correctness proof
  • Promising simulations for scalability
  • On-going and future work
  • Better metrics of performance
  • Optimizations (cache, shortcuts)
  • Combination with redondancy
  • Implementation and deployment over a real platform

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 22/22

slide-87
SLIDE 87

P2P Network Proper Greatest Common Prefix Tree Self-Stabilizing PGCP Tree Conclusion

Conclusion

  • Contributions
  • Practical P2P prefix tree maintenance
  • Comprehensive correctness proof
  • Promising simulations for scalability
  • On-going and future work
  • Better metrics of performance
  • Optimizations (cache, shortcuts)
  • Combination with redondancy
  • Implementation and deployment over a real platform

C´ edric Tedeschi Self-Stabilization in Tree-Structured P2P Service Discovery Systems 22/22