technische universität yimei liao chemnitz kurt tutschku vertretung - professur rechner- netze und...

Technische Universität

Yimei Liao Chemnitz

Kurt Tutschku Vertretung - Professur Rechner-netze und verteilte Systeme

Chord - A Distributed Hash Table

Yimei Liao


Yimei Liao Chemnitz

Outline– Lookup problem in Peer-to-Peer systems and Solutions– Chord Algorithm

• Consistent Hashing• Scalable Key Location• Node joins • Stabilization

– Summary

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Yimei Liao Chemnitz

Peer-to-Peer Systems• Peer-to-Peer System: self-organizing system of equal,

autonomous entities (peers) – Decentralized resource usage – Decentralized self-organization– Where to store? where to get?

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Solutions Centralized servers Flooding search Distributed hash tables


Yimei Liao Chemnitz

Solutions to lookup problem

– Centralized servers• Maintain the current location of data items in a central server• Central server becomes crucial• Best for simple and small applications

– Flooding search• Broadcast a request for an item among the nodes• No additional routing information• High bandwidth consumption

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Yimei Liao Chemnitz

Solutions to lookup problem– Distributed hash tables

• A global view of data distributed among many nodes • Mapping nodes and data items into a common address space• Each DHT node manages a small number of references to

other nodes• Queries are routed via a small number of nodes to the target

node• Load for retrieving items should be balanced equally among all

nodes• Robust against random failure and attacks• Provides a definitive answer to a query

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Yimei Liao Chemnitz

Chord Algorithm – Consistent Hashing

• Supports just one operation: given a key of an item, it maps the key onto a node where the item is located

• Consistent Hashing• Assign each node and key an m-bit identifier using a base

hash function such as SHA-1• Identifiers are ordered in an identifier circle modulo 2m

(Chord ring)• Key k is assigned to the first node whose identifier is equal

to or follows k: succ(k) = the node with the smallest id k

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Yimei Liao Chemnitz

Chord Algorithm – Consistent Hashing

identifier space : m=3 node key

0 1 3

7

1

2

6

6

1

2

0

4

26

5

1

3

7

identifiercircle


Yimei Liao Chemnitz

Chord Algorithm – Simple Key Lookup• Simple Key Lookup

8

1

2

6

0

4

26

5

1

3

7

Queries are passed around the circle via successor pointers

Requires traversing All nodes to find the appropriate mapping

successor(1) = 3

successor(3) = 6

successor(6) = 0

successor(0) = 1Node 0 sends a query for key 6


Yimei Liao Chemnitz

Chord Algorithm – Scalable Key Location• Finger Table

• Each node n maintains a routing table with up to m entries • The ith entry in the table at node n contains the identifier of the first

node s that succeeds n by at least 2i-1 on the identifier circle.(s = succ(n+2i-1))

• s is called the ith finger of node n

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Definition of variables for node n


Yimei Liao Chemnitz

Chord Algorithm – Scalable Key Location

For. start Int. Succ.

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Finger tablem = 3, each node n maintains at most 3 entries

0

4

26

5

1

3

7

finger table keys

0+20

0+21

0+22

124

[1,2) 336

[2,4)[4,0)

finger table keys


3+20

3+21

3+22

457

[4,5) 660

[5,7)[7,3)

1

2

finger table keys


6+20

6+21

6+22

702

[7,0) 003

[0,2)[2,6)

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Yimei Liao Chemnitz

Chord Algorithm – Scalable Key Location

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Query

• Upon receiving a query for key id, a node

Check whether it stores the item locally

If not, forwards the query to the largest node in its successor table that does not exceed id


Yimei Liao Chemnitz

Chord Algorithm – Scalable Key Locationid=5 n=7

12

0

4

26

5

1

3

7

finger table keys

start Int. Succ.1 [1,2) 32 [2,4) 34 [4,0) 4

finger table keys

start Int. Succ.4 [4,5)5 [5,7)7 [7,3)

1

2

finger table keys

start Int. Succ.0 [0,1) 01 [1,3) 33 [3,7)

6

4

Successor 0Predecessor 4

3Successor 3Predecessor 7

SuccessorPredecessor 0

finger table keys

start Int. Succ.5 [5,6) 76 [6,0) 70 [0,4) 0

Successor Predecessor 3

74

7

7

succ(5) = 7

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O(logN)

pred(k)?


Yimei Liao Chemnitz

Chord Algorithm - Node joins

• Invariants to preserve– Each node’s successor is correctly maintained– For every key k, node succ(k) is responsible for k

• It is desirable for the finger tables to be correct• Tasks to be performed by Chord

– Initialize the predecessor and fingers of node n– Update the fingers and predecessor of existing nodes to reflect

the addition of n– Notify the higher layer software so that it can transfer state

associated with keys that node n is now responsible for

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Yimei Liao Chemnitz


start Int. Succ.1 [1,2) 32 [2,4) 34 [4,0) 7

14

0

4

26

5

1

3

7

finger table keys

finger table keys

start Int. Succ.4 [4,5) 75 [5,7) 77 [7,3) 7

1

2

finger table keys

start Int. Succ.0 [0,1) 01 [1,3) 03 [3,7) 3

6

4




finger table keys

start Int. Succ.6 [6,7)7 [7,1)1 [1,5)

773

Successor Predecessor

73

Initializing fingers and predecessor

find_succ(6);


Yimei Liao Chemnitz


start Int. Succ.1 [1,2)2 [2,4)4 [4,0) 7

15

0

4

26

5

1

3

7

finger table keys

5

finger table keys

start Int. Succ.4 [4,5) 75 [5,7) 77 [7,3) 7

5

1

2

finger table keys

start Int. Succ.0 [0,1) 01 [1,3) 03 [3,7)

6

4




5

finger table keys

start Int. Succ.6 [6,7)7 [7,1)1 [1,5)

773


73

5

Updating fingers of existing nodes

33

P = find_pred(n-2i-1)i = 1, P = find_pred(4)i = 2, P = find_pred(3)i = 3, P = find_pred(1)

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O(log2N)


Yimei Liao Chemnitz


start Int. Succ.1 [1,2) 32 [2,4) 34 [4,0) 7

16

0

4

26

5

1

3

7

finger table keys

5

finger table keys

start Int. Succ.4 [4,5) 75 [5,7) 77 [7,3) 7

5

1

2

finger table keys

start Int. Succ.0 [0,1) 01 [1,3) 03 [3,7) 3

6

4




5

finger table keys

start Int. Succ.6 [6,7)7 [7,1)1 [1,5)

773


73

5

Transferring Keys


Yimei Liao Chemnitz


start Int. Succ.1 [1,2) 32 [2,4) 34 [4,0) 7

17

0

4

26

5

1

3

7

finger table keys

7

finger table keys

start Int. Succ.4 [4,5) 75 [5,7) 77 [7,3) 7

7

1

2

finger table keys

start Int. Succ.0 [0,1) 01 [1,3) 03 [3,7) 3

6

4




7

finger table keys

start Int. Succ.6 [6,7)7 [7,1)1 [1,5)

773


73

7

Query without all finger tables been updatedsucc(4) = 7


Yimei Liao Chemnitz

Chord Algorithm - Stabilization

• Stabilization– Correctness and performance– Keep node‘s successor pointers up to date– Use successor pointers to verify correct finger table entries

– Periodically node n 1) asks its successor, n’, about its predecessor n’’; 2) If n’’ is between n’ and n, then let n->successor = n’’ and repeat step 1) until we reach a point where predecessor of succ(n) = n

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Yimei Liao Chemnitz

Chord Algorithm – Node Failure

• Node Failure– Successor-list– If successor fails, replace it with the first live entry in the list– Later run stabilization to correct finger table and successor-list

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Yimei Liao Chemnitz

Summary• Characteristics of Chord

– Load balancedistributed hash table

– Decentralizationfully distributed

– Scalabilitycost of lookup grows logarithmic

– Availabilityautomatically adjusts internal tables

– Flexible namingno constraints on the structure of the keys

Routing Hops O(logN)

Arrival O(log2N)

Departure O(log2N)

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Yimei Liao Chemnitz

References• I. Stoica, R. Morris, D. Karger, F. Kaashoek, and H.

Balakrishnan. Chord: A scalable Peer-To-Peer lookup service for internet applications. In Proceedings of the 2001 ACM SIGCOMM Conference, pages 149–160, 2001.

• R. Steinmetz, K. Wehrle (Edt.): "Peer-to-Peer Systems and Applications", LNCS 3485, Springer, Chapter 7-8, 2005.

• http://www.wikipedia.org

• http://www.google.com

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Yimei Liao Chemnitz

Thank YouQuestions?

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technische universität yimei liao chemnitz kurt tutschku vertretung - professur rechner- netze und...

Documents

node key

node n slide

node s

dht node

identifier circle slide

chord ring key

i th finger of node

target node load