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On Maximum Stability with Enhanced Scalability in High-Churn DHT Deployment Junfeng Xie, Nanjing University, China Zhenhua Li, Peking University, China Guihai Chen, Nanjing University, China Jie Wu, Florida Atlantic University, USA
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Outline A relaxation Motivation Related work Grouping Strategy Maximum Stability Problem Performance Evaluation Conclusion and Future Work 2
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A relaxation Vienna – so many famous places of interest ICPP – so few audience 3
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A relaxation (cont.) Our paper has many formula Steven Hawking: “One more formula, one half audience” So I add more pictures, reduce formula 4
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Motivation P2P, DHT – hot topics in the past 10 years Why? – Utilization of Internet edge nodes Internet edge nodes Advantages: enormous – many many … so scalability Disadvantages: dynamic – join leave … so stability 5
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Motivation (cont.) A fundamental problem of P2P and DHT -- efficient leverage of dynamic nodes (dwarfs) 6
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Related Work GiantOnly – OpenDHT : giants as DHT servers, dwarfs as clients Giant ≈ Dwarf – Chord, Pastry, Tapestry, Kademila, Cycloid a giant = a DHT node, a dwarf = a DHT node Problem? scalability vs. stability 7
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Grouping Strategy Idea: 1) a giant = a DHT node 2) a group of dwarfs = a DHT node Inter-group: DHT Intra-group: random, erasure-code or replicate 8
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Grouping Strategy (cont.) Grouping Strategy’s advantages: 1)Enhanced scalability -- near Giant ≈ Dwarf 2)Maximum stability -- near GiantOnly Sweet spot between GiantOnly and Giant ≈ Dwarf 9
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Grouping Strategy (cont.) A simple example 10
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Grouping Strategy (cont.) Kernel problem: 1) how many groups? – N/logN 2) how to group? – next section 11
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Maximum Stability Problem MSG problem to minimize And 12
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Maximum Stability Problem (cont.) 1) MSG problem is NP-hard (omitted here) 2) MSG problem is infeasible – requires each node’s join and leave time So restricted MSG problem 1) homogeneous grouping – nodes within the similar dynamics are grouped 2) stochastic computation of ψ, σ and Var(ψ). 13
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Maximum Stability Problem (cont.) Homogeneous grouping 14 Session length time (stl) intervals:
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so Var(ψ) only depends on (y1, y2, …, yk, …) Assume the nodes’ join and leave form a predictable stochastic process Session length time (stl) intervals: 15 Maximum Stability Problem (cont.)
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Therefore, the restricted MSG problem is in fact: how to design the intervals (y1, y2, …, y m-1 ) so as to minimize Var(ψ)? -- Solution: Matlab function fminsearch(Var, y1, y2, …) 16
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Performance Evaluation Grouping snapshot (sorted by stl intervals) 17
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Performance Evaluation (cont.) Stability (churn rate) 18
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Performance Evaluation (cont.) Scalability (storage capacity) 19
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Conclusion and Future Work Conclusion: A homogeneous grouping strategy, which can achieve maximum stability and enhanced scalability Problems: 1) Heterogeneous grouping? 2) Fast optimization algorithm 20
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The End 21
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