Chord - A Distributed Hash Table

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1 Kurt Tutschku Vertretung - Professur Rechnernetze und verteilte Systeme Chord - A Distributed Hash Table

2 Outline Lookup problem in Peer-to-Peer systems and Solutions Chord Algorithm Consistent Hashing Scalable Key Location Node joins Stabilization Summary

3 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

4 Solutions to lookup problem centralized servers Maintain the current location of data items in a central server Search complexity O() 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(N ) Results are not guaranteed

5 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 5

6 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- Identifiers are ordered in an identifier circle modulo m (Chord ring) Key k is assigned to the first node whose identifier is equal to or follows k.

7 Chord Algorithm Consistent Hashing identifier space : m= node key 0 0 identifier circle 5

8 Chord Algorithm Simple Key Lookup Simple Key Lookup Queries are passed around the circle via successor pointers Requires traversing all Nodes to find the appropriate mapping Node 0 sends a query for key successor(0) = 0 successor() = successor() = 0 5 successor() = 8

9 Chord Algorithm Scalable Key Location Finger Table Each node n maintains a routing table with up to m entries The i th entry in the table at node n contains the identifier of the first node s that succeeds n by at least i- on the identifier circle.(s = successor(n+ i- )). s is called the i th finger of node n. Definition of variables for node n 9

10 Chord Algorithm Scalable Key Location Finger table m =, each node n maintains at most entries For. + 0 [,0) [0,) + [,) For [,) 0+ [,) 0+ [,0) 5 For. + 0 [,5) + 5 [5,) + [,) 0 0

11 Chord Algorithm Scalable Key Location Pseudocode to find the successor node of an identifier Find id s successor by finding the immediate predecessor of the id Walk clockwise to find the node which precedes id and whose successor succeeds id Start with the m th finger of node n See if it comes between node n and the id, if not, check the m- th finger until we find one wich does. This is the closest node preceding id among all the fingers of n

12 Chord Algorithm Scalable Key Location id=5 n= 0 [0,) 0 [,) 0 [,) Successor 0 Predecessor 0 [,) [,) [,0) Successor Predecessor 5 [5,) [,0) 0 [0,) 0 successor(5) = 5 [,5) 5 [5,) [,) Successor Predecessor 0 Successor Predecessor O(logN)

13 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

14 Chord Algorithm - Node joins Initializing fingers and predecessor 0 [0,) 0 [,) 0 [,) Successor 0 Predecessor 5 find_successor(); 0 [,) [,) [,0) Successor Predecessor [,) [,) [,5) 5 [,5) 5 [5,) [,) Successor Predecessor 0 Successor Predecessor

15 Chord Algorithm - Node joins Updating fingers of existing nodes 0 [0,) 0 [,) 0 [,) Successor 0 Predecessor 5 0 [,) [,) [,0) 5 Successor Predecessor [,) [,) [,5) Successor Predecessor 5 P = find_predecessor(n- i- ) i =, P = find_predecessor() i =, P = find_predecessor() O(log N) i =, P = find_predecessor() [,5) 5 5 [5,) 5 [,) Successor 5 Predecessor 0 5

16 Chord Algorithm - Node joins Transferring Keys 0 [0,) 0 [,) 0 [,) Successor 0 Predecessor 5 0 [,) [,) [,0) Successor Predecessor [,) [,) [,5) Successor Predecessor 5 [,5) 5 5 [5,) 5 [,) Successor 5 Predecessor 0

17 Chord Algorithm node joins Pseudocode for the node join operation

18 Chord Algorithm - Stabilization Stabilization Correctness and performance Keep node s successor pointers up to date Use successor pointers to verify correct finger table entries 8

19 Pseudocode for stabilization Chord Algorithm - Stabilization Join does not make the rest of the network aware of n Every node runs stabilize periodically, to verify the successor Node n asks its successor for the successor s predecessor x. See if x should be n s successor instead. (happens if x recently joined the system) Notify n s successor of n s exist. Successor changes its predecessor to n if it knows no closer predecessor than n. Use successor pointers to update finger tables. 9

20 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 0

21 Summary Characteristics of Chord Load balance distributed hash table Decentralization fully distributed Scalability cost of lookup grows logarithmic Routing Hops O(logN) Arrival O(log N) Departure O(log N) Availability automatically adjusts internal tables Flexible naming no constrains on the structure of the keys

22 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 00 ACM SIGCOMM Conference, pages 9 0, 00. R. Steinmetz, K. Wehrle (Edt.): "Peer-to-Peer Systems and Applications", LNCS 85, Springer, Chapter -8,

23 Thank You Questions?

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