Chord: A Scalable Peer-to-Peer Lookup Service for Internet Applications

1. Chord: A Scalable Peer-to-Peer Lookup Service for Internet Applications Ion Stoica Robert Morris David Liben-Nowell David R. Karger M. Frans Kaashoek Frank Dabek Hari Balakrishnan Presented By- Manan Rawal, Bhaskar Gupta

2. Introduction • Efficient lookup of a node which stores data items for a particular search key. • Provides only one operation: given a key, it maps the key onto a node. • Example applications: • Co-operative Mirroring • Time-shared storage • Distributed indexes • Large-Scale combinatorial search

3. Problems addressed • Load Balance: Distributed hash function spreads keys evenly over the nodes • Decentralization: Fully distributed • Scalability: Lookup grows as a log of number of nodes • Availability: Automatically adjusts internal tables to reflect changes. • Flexible Naming: No constraints on key structure.

4. Chord Protocol • Assumes communication in underlying network is both symmetric and transitive. • Assigns keys to nodes with consistent hashing • Hash function balances the load • When Nth node joins or leaves only O(1/N) fraction of keys moved.

5. Chord protocol • Consistent hashing function assigns each node and key an m-bit identifier using SHA-1 base hash function. • Node’s IP address is hashed. • Identifiers are ordered on a identifier circle modulo 2m called a chord ring. • succesor(k) = first node whose identifier is >= identifier of k in identifier space.

6. Chord protocol m = 6 10 nodes

7. Theorem • For any set of N nodes and K keys, with high probability: • Each node is responsible for at most (1+e)K/N keys. • When an (N+1)st node joins or leaves the network, responsibility for O(K/N) keys changes hands. e = O(log N)

8. Simple Key Location Scheme N1 N8 K45 N48 N14 N42 N38 N21 N32

9. Scalable Lookup Scheme N1 Finger Table for N8 N56 N8 N51 finger 6 finger 1,2,3 N48 N14 finger 5 N42 finger 4 N38 finger [k] = first node that succeeds (n+2k-1)mod2m N21 N32

10. Scalable Lookup Scheme // ask node n to find the successor of id n.find_successor(id) if (id belongs to (n, successor]) return successor; else n0 = closest preceding node(id); return n0.find_successor(id); // search the local table for the highest predecessor of id n.closest_preceding_node(id) for i = m downto 1 if (finger[i] belongs to (n, id)) return finger[i]; return n;

11. Lookup Using Finger Table N1 lookup(54) N56 N8 N51 N48 N14 N42 N38 N21 N32

12. Scalable Lookup Scheme • Each node forwards query at least halfway along distance remaining to the target • Theorem: With high probability, the number of nodes that must be contacted to find a successor in a N-node network is O(log N)

13. Dynamic Operations and Failures Need to deal with: • Node Joins and Stabilization • Impact of Node Joins on Lookups • Failure and Replication • Voluntary Node Departures

14. Node Joins and Stabilization • Node’s successor pointer should be up to date • For correctly executing lookups • Each node periodically runs a “Stabilization” Protocol • Updates finger tables and successor pointers

15. Node Joins and Stabilization • Contains 6 functions: • create() • join() • stabilize() • notify() • fix_fingers() • check_predecessor()

16. Create() • Creates a new Chord ring n.create() predecessor = nil; successor = n;

17. Join() • Asks m to find the immediate successorof n. • Doesn’t make rest of the networkaware of n. n.join(m) predecessor = nil; successor = m.find_successor(n);

18. Stabilize() • Called periodically to learn about new nodes • Asks n’s immediate successor about successor’s predecessor p • Checks whether p should be n’s successor instead • Also notifies n’s successor about n’s existence, so that successor may change its predecessor to n, if necessary n.stabilize() x = successor.predecessor; if (x  (n, successor)) successor = x; successor.notify(n);

19. Notify() • m thinks it might be n’s predecessor n.notify(m) if (predecessor is nil or m  (predecessor, n)) predecessor = m;

20. Fix_fingers() • Periodically called to make sure that fingertable entries are correct • New nodes initializetheir finger tables • Existing nodes incorporatenew nodes into their finger tables n.fix_fingers() next = next + 1 ; if (next > m) next = 1 ; finger[next] = find_successor(n + 2next-1);

21. Check_predecessor() • Periodically called to check whether predecessor has failed • If yes, it clears the predecessor pointer, which can then be modified by notify() n.check_predecessor() if (predecessor has failed) predecessor = nil;

22. Theorem 3 • If any sequence of join operations is executed interleaved with stabilizations, then at some time after the last join the successor pointers will form a cycle on all nodes in the network

23. Stabilization Protocol • Guarantees to add nodes in a fashion to preserve reach ability • By itself won’t correct a Chord system that has split into multiple disjoint cycles, or a single cycle that loops multiple times around the identifier space

24. Impact of Node Joins on Lookups • Correctness • If finger table entries are reasonably current • Lookup finds the correct successor in O(log N) steps • If successor pointers are correct but finger tables are incorrect • Correct lookup but slower • If incorrect successor pointers • Lookup may fail

25. Impact of Node Joins on Lookups • Performance • If stabilization is complete • Lookup can be done in O(log N) time • If stabilization is not complete • Existing nodes finger tables may not reflect the new nodes • Doesn’t significantly affect lookup speed • Newly joined nodes can affect the lookup speed, if the new nodes ID’s are in between target and target’s predecessor • Lookup will have to be forwarded through the intervening nodes, one at a time

26. Theorem 4 • If we take a stable network with N nodes with correct finger pointers, and another set of up to N nodes joins the network, and all successor pointers (but perhaps not all finger pointers) are correct, then lookups will still take O(log N) time with high probability

27. Failure and Replication • Correctness of the protocol relies on the fact of knowing correct successor • To improve robustness • Each node maintains a successor list of ‘r’ nodes • This can be handled using modified version of stabilize procedure • Also helps higher-layer software to replicate data

28. Theorem 5 • If we use successor list of length r = O(log N) in a network that is initially stable, and then every node fails with probability ½, then with high probability find_successor returns the closest living successor to the query key

29. Theorem 6 • In a network that is initially stable, if every node fails with probability ½, then the expected time to execute find_successor is O(log N)

30. Voluntary Node Departures • Can be treated as node failures • Two possible enhancements • Leaving node may transfers all its keys to its successor • Leaving node may notify its predecessor and successor about each other so that they can update their links

31. Conclusion • Efficient location of the node that stores a desired data item is a fundamental problem in P2P networks • Chord protocol solves it in a efficient decentralized manner • Routing information: O(log N) nodes • Lookup: O(log N) nodes • Update: O(log2 N) messages • It also adapts dynamically to the topology changes introduced during the run

32. Future Work • Using Chord to detect and heal partitions whose nodes know of each other. • Every node should know of some same set of initial nodes • Nodes should maintain long-term memory of a random set of nodes that they have visited earlier • Malicious set of Chord participants could present an incorrect view of the Chord ring • Node n periodically asks other nodes to do a lookup for n

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