Technische Universität Chemnitz
Kurt Tutschku Vertretung - Professur Rechner-netze und verteilte Systeme
Chord - A Distributed Hash Table
Yimei Liao
Hauptseminar „Peer-to-Peer Networks“ 2
Technische Universität
Yimei Liao Chemnitz
Outline
Lookup problem in Peer-to-Peer systems and Solutions Chord Algorithm
– Consistent Hashing
– Scalable Key Location
– Node joins
– Stabilization Summary
Hauptseminar „Peer-to-Peer Networks“ 3
Technische Universität
Yimei Liao Chemnitz
Peer-to-Peer Systems
Peer-to-Peer System: self-organizing system of equal, autononous entities (peers) decentralized resource usage decentraliced self-organization where to store? where to get?
Solutions centralized servers flooding search distributed Hash Tables
Hauptseminar „Peer-to-Peer Networks“ 4
Technische Universität
Yimei Liao Chemnitz
Solutions to lookup problem
centralized servers– Maintain the current location of data items in a central server– Search complexity O(1)– Central server becomes crucial– Best for simple and small applications
flooding search– Broadcast a request for an item among the nodes– No additional routing informations– High bandwidth consumption– Search complexity O(N2)– Results are not guaranteed
Hauptseminar „Peer-to-Peer Networks“ 5
Technische Universität
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 about results
Hauptseminar „Peer-to-Peer Networks“ 6
Technische Universität
Yimei Liao Chemnitz
Chord Algorithm – Consistent Hashing
supports just one operation: given a key, it maps the key onto a node.
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.
Hauptseminar „Peer-to-Peer Networks“ 7
Technische Universität
Yimei Liao Chemnitz
Chord Algorithm – Consistent Hashing
identifier space : m=3
node key
0
1
3
1
2
6
6
1
2
0
4
26
5
1
3
7
identifiercircle
Hauptseminar „Peer-to-Peer Networks“ 8
Technische Universität
Yimei Liao Chemnitz
Chord Algorithm – Simple Key Lookup
Simple Key Lookup
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
Hauptseminar „Peer-to-Peer Networks“ 9
Technische Universität
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 = successor(n+2i-1)).
– s is called the ith finger of node n.
Definition of variables for node n
Hauptseminar „Peer-to-Peer Networks“ 10
Technische Universität
Yimei Liao Chemnitz
Chord Algorithm – Scalable Key Location
Finger tablem = 3, each node n maintains at most 3 entries
0
4
26
5
1
3
7
finger table keys
For. start Int. Succ.
0+20
0+21
0+22
124
[1,2) 336
[2,4)[4,0)
finger table keys
For. start Int. Succ.
3+20
3+21
3+22
457
[4,5) 660
[5,7)[7,3)
1
2
finger table keys
For. start Int. Succ.
6+20
6+21
6+22
702
[7,0) 003
[0,2)[2,6)
5
Hauptseminar „Peer-to-Peer Networks“ 11
Technische Universität
Yimei Liao Chemnitz
Chord Algorithm – Scalable Key Location
Pseudocode to find the successor node of an identifier
Walk clockwise to find the node which precedes id and whose successor succeeds id
Start with the mth finger of node nSee if it comes between node n and the id, if not, check the m-1th
finger until we find one wich does.This is the closest node preceding idamong all the fingers of n
Find id’s successor by finding the immediate predecessor of the id
Hauptseminar „Peer-to-Peer Networks“ 12
Technische Universität
Yimei Liao Chemnitz
Chord Algorithm – Scalable Key Location
id=5
n=7
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) 03 [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
successor(5) = 7
4
O(logN)
Hauptseminar „Peer-to-Peer Networks“ 13
Technische Universität
Yimei Liao Chemnitz
Chord Algorithm - Node joins
Invariants to be preserve Each node’s successor is correctly maintained For every key k, node successor(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
Hauptseminar „Peer-to-Peer Networks“ 14
Technische Universität
Yimei Liao Chemnitz
Chord Algorithm - Node joins
0
4
26
5
1
3
7
finger table keys
start Int. Succ.1 [1,2) 32 [2,4) 34 [4,0) 7
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
Successor 0Predecessor 35
Successor 3Predecessor 6
Successor 6Predecessor 0
finger table keys
start Int. Succ.6 [6,7)7 [7,1)1 [1,5)
773
Successor Predecessor
73
Initializing fingers and predecessor
find_successor(6);
Hauptseminar „Peer-to-Peer Networks“ 15
Technische Universität
Yimei Liao Chemnitz
Chord Algorithm - Node joins
0
4
26
5
1
3
7
finger table keys
start Int. Succ.1 [1,2)2 [2,4)4 [4,0) 75
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
Successor 0Predecessor 35
Successor 3Predecessor 6
Successor 7Predecessor 0
5
finger table keys
start Int. Succ.6 [6,7)7 [7,1)1 [1,5)
773
Successor Predecessor
73
5
Updating fingers of existing nodes
33
P = find_predecessor(n-2i-1)i = 1, P = find_predecessor(4)i = 2, P = find_predecessor(3)i = 3, P = find_predecessor(1)
3
O(log2N)
Hauptseminar „Peer-to-Peer Networks“ 16
Technische Universität
Yimei Liao Chemnitz
Chord Algorithm - Node joins
0
4
26
5
1
3
7
finger table keys
start Int. Succ.1 [1,2) 32 [2,4) 34 [4,0) 76
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
Successor 0Predecessor 35
Successor 3Predecessor 6
Successor 6Predecessor 0
5
finger table keys
start Int. Succ.6 [6,7)7 [7,1)1 [1,5)
773
Successor Predecessor
73
5
Transferring Keys
Hauptseminar „Peer-to-Peer Networks“ 17
Technische Universität
Yimei Liao Chemnitz
Chord Algorithm – node joins
Pseudocode for the node join operation
Hauptseminar „Peer-to-Peer Networks“ 18
Technische Universität
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
Hauptseminar „Peer-to-Peer Networks“ 19
Technische Universität
Yimei Liao Chemnitz
Chord Algorithm - Stabilization
Pseudocode for stabilization
Join does not make the rest of the network aware of n
Every node runs stabilizeperiodically, to verify the successor
Use successor pointers toupdate finger tables.
Node n asks its successor forthe successor’s predecessor x.See if x should be n’s successorinstead. (happens if x recently joined the system)
Notify n’s successor of n’sexist. Successor changes its predecessor to n if itknows no closer predecessor than n.
Hauptseminar „Peer-to-Peer Networks“ 20
Technische Universität
Yimei Liao Chemnitz
Chord Algorithm – Node Failure
Node Failure Successor-list If successor fails, replaces it with the first live entry in the list Later run stabilize to correct finger table and successor-list
Hauptseminar „Peer-to-Peer Networks“ 21
Technische Universität
Yimei Liao Chemnitz
Summary
Characteristics of Chord Load balance
distributed hash table Decentralization
fully distributed Scalability
cost of lookup grows logarithmic
Availabilityautomatically adjusts internal tables
Flexible namingno constrains on the structure of the keys
Routing Hops O(logN)
Arrival O(log2N)
Departure O(log2N)
Hauptseminar „Peer-to-Peer Networks“ 22
Technische Universität
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.
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