1. 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

2. Outline A relaxation Motivation Related work Grouping Strategy Maximum Stability Problem Performance Evaluation Conclusion and Future Work 2

3. A relaxation Vienna – so many famous places of interest ICPP – so few audience  3

4. A relaxation (cont.) Our paper has many formula Steven Hawking: “One more formula, one half audience” So  I add more pictures, reduce formula 4

5. 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

6. Motivation (cont.) A fundamental problem of P2P and DHT -- efficient leverage of dynamic nodes (dwarfs) 6

7. 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

8. 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

9. 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

10. Grouping Strategy (cont.) A simple example 10

11. Grouping Strategy (cont.) Kernel problem: 1) how many groups? – N/logN 2) how to group? – next section 11

12. Maximum Stability Problem MSG problem to minimize And 12

13. 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

14. Maximum Stability Problem (cont.) Homogeneous grouping 14 Session length time (stl) intervals:

15. 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.)

16. 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

17. Performance Evaluation Grouping snapshot (sorted by stl intervals) 17

18. Performance Evaluation (cont.) Stability (churn rate) 18

19. Performance Evaluation (cont.) Scalability (storage capacity) 19

20. 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

21. The End 21