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Achieving One-Hop DHT Lookup and Strong Stabilization by Passing Tokens

Ben Leong and Ji Li MIT Computer Science and Artificial Intelligence Laboratory

{benleong, jli}@mit.edu

Achieving One-Hop DHT Lookup and Strong Stabilization by Passing Tokens – p.1

Structured Peer-to-Peer Systems

Large scale dynamic network Overlay infrastructure : Scalable Self configuring Fault tolerant Every node responsible for some objects Find node having desired object Challenge: Efficient Routing at Low Cost

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Address Space

N15 N10 N17 N20 N25 N30 N35 N40 N47 N51 N57 N62 N0 N6 K13 K2 K47 K32 K52 K54 N49

Most common — one-dimensional circular address space

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Distributed Hash Tables (DHTs)

A Distributed Hash Table (DHT) is a distributed data structure that supports a put/get interface. Store and retrieve {key, value} pairs efficiently

• ver a network of (generally unreliable) nodes

Early DHTs stored very little state (O(log n)) to cope with network churn (Stoica et al., 2001; Ratnasamy et al., 2001; Zhao et al., 2001; Rowstron and Druschel, 2001).

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Distributed Hash Tables (DHTs)

Keep state stored per node small because of network churn ⇒ minimize book-keeping & maintenance traffic Storage is cheap, so it is entirely reasonable to store a global lookup table at every node to achieve one-hop lookup (Gupta et al., 2004) Problem: Getting the routing information to all nodes and keeping it up-to-date

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Anjali’s One-Hop Scheme (NDSI ’04)

Hierarchical scheme Divide ring into slices – node at midpoint is the slice leader Slices further divided into units with leaders Slice leaders communicate with each other and with unit leaders in slice Information progagated along ring on stay-a-live messages

Achieving One-Hop DHT Lookup and Strong Stabilization by Passing Tokens – p.6

Anjali’s One-Hop Scheme

Problems: Slice leaders significantly more bandwidth than the other nodes Several parameters — tuning requires knowledge of steady state network size Natural question: why don’t we just use per-event ad hoc broadcast trees?

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Token Passing Algorithm

Token – message containing join or leave information (IP address, id). Also has a range of propagation, specified by destination nd. When a node receives a token, it can: Pass the token to its predecessor; or Generate q secondary tokens that cover the remaining propagation range.

Achieving One-Hop DHT Lookup and Strong Stabilization by Passing Tokens – p.8

Token Passing Algorithm

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Token Passing Algorithm

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Token Passing Algorithm

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Token Passing Algorithm

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Token Passing Algorithm

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Token Passing Algorithm

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Token Passing Algorithm

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Token Passing Algorithm

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Pick q nodes in total

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Token Passing Algorithm

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Pass last token to predecessor

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Token Passing Algorithm

Address space can be decomposed recursively Token is destroyed when it reaches its destination Nodes do not necessarily have to use a fixed q Tokens can be merged to save on propagation overhead

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Lookup Algorithm

Just contact the best known successor. It’s probably the right one; if not, it will tell you where to go. Correctness of routing is guaranteed by correctness of successor/predecessor pointers In worst case, simply follow a chain of successor pointers – slow but correct. Stabilization – process that maintains and repairs successor/predecessor pointers

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Definitions

We say that the network is

• 1. weakly stable if, for all nodes u, we

have predecessor(successor(u)) = u;

• 2. strongly stable if, in addition, for each

node u, there is no node v such that u < v < successor(u); and

• 3. loopy if it is weakly but not strongly

stable (see (Stoica et al., 2002)).

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Weak Stabilization

Nodes periodically probe their immediate neighbors and exchange successor/predecessor lists All messages contain IP address, port number and node id

Theorem 1 The weak stabilization protocol

will eventually cause our network to converge to a weakly stable state.

Achieving One-Hop DHT Lookup and Strong Stabilization by Passing Tokens – p.21

Loopy Example

N60 N45 N36 N24 N79 N86 N10

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Strong Stabilization

p p

p

Key idea: to detect loops, all we need to do is to traverse the entire ring and make sure that we come back to where we started

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Strong Stabilization

Theorem 2 The combination of our parallel

token-passing algorithm with the weak stabilization protocol will cause our network to converge to a strongly stable state within at most O(n2) rounds of token-passing. Take any set of r nodes and have them send a message to the consecutive node. If a loop exists, at least one pair will detect it. Key Insight: this property does not change if you choose the r nodes recursively.

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Simulation Results

Analysis shows that our scheme is feasible in terms of bandwidth consumption under realistic assumptions Implemented algorithm in p2psim and compared it directly to Anjali’s scheme Parameters: Node lifetime: 60 mins Avg 10 node joins per second for 200 s. Nodes rejoin after mean interval of 6 mins Query rate — 1 per sec per node

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One-Hop Failure Rates

0.02 0.04 0.06 0.08 0.1 200 250 300 350 400 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 Network Size Gupta et al. Token Passing

Lookup failure rate Network Size Time (s)

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Two-Hop Failure Rates

0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 0.0018 200 250 300 350 400 Gupta et al. Token Passing

Lookup failure rate Time (s)

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Bandwidth Consumption

5 10 15 20 25 30 35 240 260 280 300 320 340 360 380 400 Gupta et al. - slice leaders Gupta et al. - regular node Token passing

Bandwidth consumption per node (kbps) Time (s)

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Related Work

One-Hop (Gupta et al., 2004) Superpeers (Mizrak et al., 2003) Kelips (Gupta et al., 2003)

Achieving One-Hop DHT Lookup and Strong Stabilization by Passing Tokens – p.29

Conclusion

Performs as well as Anjali’s scheme Simplicity Imposes a slightly higher average overhead, but imposes uniform load Can vary q to adapt to network heterogeneity Have strong stabilization as a side-effect

Achieving One-Hop DHT Lookup and Strong Stabilization by Passing Tokens – p.30

Achieving One-Hop DHT Lookup and Strong Stabilization by Passing Tokens

Ben Leong and Ji Li MIT Computer Science and Artificial Intelligence Laboratory

{benleong, jli}@mit.edu

Achieving One-Hop DHT Lookup and Strong Stabilization by Passing Tokens – p.31

Fault Tolerance

Sometimes bad things happen and a token is lost. Missing information is discovered during lookup process Observation: a lost token results in a consecutive segment of the address space missing some piece of information Solution: propagate repair tokens Passed in both directions Cannot be split

Achieving One-Hop DHT Lookup and Strong Stabilization by Passing Tokens – p.32

Repair

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Repair

ENTIRE SEGMENT MISSING INFORMATION

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Repair

Problem discovered!

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Repair

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References

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• R. (2003). Kelips: Building an efficient and stable P2P DHT

through increased memory and background overhead. In Proceedings of the 2nd International Workshop on Peer-to- Peer Systems (IPTPS ’03). Mizrak, A., Cheng, Y., Kumar, V., and Savage, S. (2003). Structured superpeers: Leveraging heterogeneity to provide constant-time lookup. In Proceedings of the 4th IEEE Work- shop on Internet Applications. Ratnasamy, S., Francis, P ., Handley, M., Karp, R., and Shenker,

• S. (2001). A scalable content-addressable network. In Pro-

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ACM SIGCOMM Conference, pages 149–160. Stoica, I., Morris, R., Liben-Nowell, D., Karger, D., Kaashoek,

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., Dabek, F ., and Balakrishnan, H. (2002). Chord: A scalable peer-to-peer lookup service for internet applica-

• tions. Technical report, MIT LCS.

Zhao, B. Y., Kubiatowicz, J. D., and Joseph, A. D. (2001). Tapestry: An infrastructure for fault-tolerant wide-area loca- tion and routing. Technical Report UCB/CSD-01-1141, UC Berkeley. 36-2