1. Technische Universität Chemnitz Kurt Tutschku Vertretung - Professur Rechner- netze und verteilte Systeme Chord - A Distributed Hash Table Yimei Liao

2. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 2 Outline  Lookup problem in Peer-to-Peer systems and Solutions  Chord Algorithm –Consistent Hashing –Scalable Key Location –Node joins –Stabilization  Summary

3. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 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. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 4 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(N 2 ) –Results are not guaranteed

5. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 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

6. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 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-1 –Identifiers are ordered in an identifier circle modulo 2 m (Chord ring) –Key k is assigned to the first node whose identifier is equal to or follows k.

7. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 7 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 identifier circle

8. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 8 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) = 1 Node 0 sends a query for key 6

9. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 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 2 i-1 on the identifier circle.(s = successor(n+2 i-1 )). –s is called the i th finger of node n.  Definition of variables for node n

10. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 10 Chord Algorithm – Scalable Key Location Finger table m = 3, each node n maintains at most 3 entries 0 4 26 5 1 3 7 finger table keys For.startInt.Succ. 0+2 0 0+2 1 0+2 2 124124 [1,2)3 3 6 [2,4) [4,0) finger table keys For.startInt.Succ. 3+2 0 3+2 1 3+2 2 457457 [4,5)6 6 0 [5,7) [7,3) 1 2 finger table keys For.startInt.Succ. 6+2 0 6+2 1 6+2 2 702702 [7,0)0 0 3 [0,2) [2,6) 5

11. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 11 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 m th finger of node n See if it comes between node n and the id, if not, check the m-1 th finger until we find one wich does. This is the closest node preceding id among all the fingers of n Find id’s successor by finding the immediate predecessor of the id

12. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 12 Chord Algorithm – Scalable Key Location id=5 n=7 0 4 26 5 1 3 7 finger table keys startInt.Succ. 1 [1,2) 3 2 [2,4) 3 4 [4,0) 4 finger table keys startInt.Succ. 4[4,5) 5[5,7) 7[7,3) 1 2 finger table keys startInt.Succ. 0[0,1)0 1[1,3)0 3[3,7) 6 4 Successor 0 Predecessor 4 3 Successor 3 Predecessor 7 Successor Predecessor 0 finger table keys startInt.Succ. 5[5,6)7 6[6,0)7 0[0,4)0 Successor Predecessor 3 7 4 7 7 successor(5) = 7 4 O(logN)

13. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 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. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 14 Chord Algorithm - Node joins 0 4 26 5 1 3 7 finger table keys startInt.Succ. 1 [1,2) 3 2 [2,4) 3 4 [4,0) 7 finger table keys startInt.Succ. 4[4,5)7 5[5,7)7 7[7,3)7 1 2 finger table keys startInt.Succ. 0[0,1)0 1[1,3)0 3[3,7)3 6 4 Successor 0 Predecessor 3 5 Successor 3 Predecessor 6 Successor 6 Predecessor 0 finger table keys startInt.Succ. 6[6,7) 7[7,1) 1[1,5) 7 7 3 Successor Predecessor 7 3 Initializing fingers and predecessor find_successor(6);

15. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 15 Chord Algorithm - Node joins 0 4 26 5 1 3 7 finger table keys startInt.Succ. 1 [1,2) 2 [2,4) 4 [4,0) 7 5 finger table keys startInt.Succ. 4[4,5)7 5[5,7)7 7[7,3)7 5 1 2 finger table keys startInt.Succ. 0[0,1)0 1[1,3)0 3[3,7) 6 4 Successor 0 Predecessor 3 5 Successor 3 Predecessor 6 Successor 7 Predecessor 0 5 finger table keys startInt.Succ. 6[6,7) 7[7,1) 1[1,5) 7 7 3 Successor Predecessor 7 3 5 Updating fingers of existing nodes 3 3 P = find_predecessor(n-2 i-1 ) i = 1, P = find_predecessor(4) i = 2, P = find_predecessor(3) i = 3, P = find_predecessor(1) 3 O(log 2 N)

16. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 16 Chord Algorithm - Node joins 0 4 26 5 1 3 7 finger table keys startInt.Succ. 1 [1,2) 3 2 [2,4) 3 4 [4,0) 7 6 finger table keys startInt.Succ. 4[4,5)7 5[5,7)7 7[7,3)7 5 1 2 finger table keys startInt.Succ. 0[0,1)0 1[1,3)0 3[3,7)3 6 4 Successor 0 Predecessor 3 5 Successor 3 Predecessor 6 Successor 6 Predecessor 0 5 finger table keys startInt.Succ. 6[6,7) 7[7,1) 1[1,5) 7 7 3 Successor Predecessor 7 3 5 Transferring Keys

17. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 17 Chord Algorithm – node joins Pseudocode for the node join operation

18. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 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

19. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 19 Chord Algorithm - Stabilization Pseudocode for stabilization Join does not make the rest of the network aware of n Every node runs stabilize periodically, to verify the successor Use successor pointers to update finger tables. 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.

20. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 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

21. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 21 Summary  Characteristics of Chord  Load balance distributed hash table  Decentralization fully distributed  Scalability cost of lookup grows logarithmic  Availability automatically adjusts internal tables  Flexible naming no constrains on the structure of the keys Routing HopsO(logN) ArrivalO(log 2 N) DepartureO(log 2 N)

22. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 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 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

23. Hauptseminar „Peer-to-Peer Networks“ Technische Universität Yimei Liao Chemnitz 23 Thank You Questions?