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Search and Replication in Unstructured Peer-to-Peer Networks

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). Disclaimer. Results, statements, opinions in this talk do not represent Cisco in anyway

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Search and Replication in Unstructured Peer-to-Peer Networks

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  1. 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)

  2. 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

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

  4. 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

  5. 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: Doesn’t scale

  6. 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

  7. 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

  8. 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!

  9. Evaluation Methodologies Simulation based: • Network topology • Distribution of object popularity • Distribution of replication density of objects

  10. 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)

  11. Modeling Methods • Object popularity distribution pi • Uniform • Zipf-like • Object replication density distribution ri • Uniform • Proportional: ri pi • Square-Root: ri  pi

  12. Evaluation Metrics • Overhead: average # of messages per node per query • Probability of search success: Pr(success) • Delay: # of hops till success

  13. 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

  14. Duplication in Flooding-Based Searches • Duplication increases as TTL increases in flooding • Worst case: a node A is interrrupted by N * q * degree(A) messages 1 3 2 4 6 5 7 8 . . . . . . . . . . . .

  15. Duplications in Various Network Topologies

  16. Relationship between TTL and Search Successes

  17. 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

  18. Idea #1: Adaptively Adjust TTL • “Expanding Ring” • Multiple floods: start with TTL=1; 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

  19. Limitations of Expanding Ring

  20. 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 N*T steps • When to terminate the search: check back with the query originator once every C steps

  21. Search Traffic Comparison

  22. Search Delay Comparison

  23. Lessons Learnt about Search Methods • Adaptive termination • Minimize message duplication • Small expansion in each step

  24. Flexible Replication • In unstructured systems, search success is essentially about coverage: visiting enough nodes to probabilistically find the object => replication density matters • Limited node storage => what’s the optimal replication density distribution? • In Gnutella, only nodes who query an object store it => ri pi • What if we have different replication strategies?

  25. Optimal ri Distribution • Goal: minimize ( pi/ ri ), where  ri =R • Calculation: • introduce Lagrange multiplier , find ri and  that minimize: ( pi/ ri ) +  * ( ri - R) =>  - pi/ ri2 = 0 for all i => ri  pi

  26. 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

  27. 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

  28. 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

  29. Distribution of ri

  30. Total Search Message Comparison • Observation: path replication is slightly inferior to random replication

  31. Search Delay Comparison

  32. Summary • Multi-walker random walk scales much better than flooding • It won’t 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

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