Principles of Reliable Distributed Systems Lecture 2: Distributed Hash Tables (DHT), Chord

1. Principles of Reliable Distributed SystemsLecture 2: Distributed Hash Tables (DHT), Chord Spring 2008 Idit Keidar

2. Today’s Material • Chord: A Scalable Peer-to-peer Lookup Service for Internet Applications • Stoica et al.

3. Reminder: Peer-to-Peer Lookup • Insert (key, file) • Lookup (key) • Should find keys inserted in any node

4. Reminder: Overlay Networks • A virtual structure imposed over the physical network (e.g., the Internet) • over the Internet, there is a (IP level) link between every pair of nodes • an overlay uses a fixed subset of these • Why restrict to a subset?

5. Routing/Lookup in Overlays • How does one route a packet to its destination in an overlay? • How about lookup (key)? • Unstructuredoverlay: (last week) • Flooding or random walks • Structuredoverlay: (today) • The links are chosen according to some rule • Tables define next-hop for routing and lookup

6. Structured Lookup Overlays • Many academic systems – • CAN, Chord , D2B, Kademlia, Koorde, Pastry, Tapestry, Viceroy, … • OverNet based on the Kademlia algorithm • Symmetric, no hierarchy • Decentralized self management • Structured overlay – data stored in a defined place, search goes on a defined path • Implement Distributed Hash Table (DHT) abstraction

7. Reminder: Hashing • Data structure supporting the operations: • void insert( key, item ) • item search( key ) • Implementation uses hash function for mapping keys to array cells • Expected search time O(1) • provided that there are few collisions

8. Distributed Hash Tables (DHTs) • Nodes store table entries • The role of array cells • Good abstraction for lookup? • Why?

9. The DHT Service Interface lookup( key ) returns the location of the node currently responsible for this key key is usually numeric (in some range)

10. Using the DHT Interface • How do you publish a file? • How do you find a file? • Requirements for an application being able to use DHTs? • Data identified with unique keys • Nodes can (agree to) store keys for each other • location of object (pointer) or actual object (data)

11. What Does a DHT Implementation Need to Do? • Map keys to nodes • Needs to be dynamic as nodes join and leave • How does this affect the service interface? • Route a request to the appropriate node • Routing on the overlay

12. (K1,V1) K V K V K V K V K V K V K V K V K V K V K V K V lookup(K1) Lookup Example insert(K1,V1)

13. Mapping Keys to Nodes • Goal: load balancing • Why? • Typical approach: • Give an m-bit id to each node and each key (e.g., using SHA-1 on the key, IP address) • Map key to node whose id is “close” to the key (need distance function) • How is load balancing achieved?

14. Routing Issues • Each node must be able to forward each lookup query to a node closer to the destination • Maintain routing tables adaptively • Each node knows some other nodes • Must adapt to changes (joins, leaves, failures) • Goals?

15. Handling Join/Leave • When a node joins it needs to assume responsibility for some keys • Ask the application to move these keys to it • How many keys will need to be moved? • When a nodes fails or leaves, its keys have to be moved to others • What else is needed in order to implement this?

16. P2P System Interface • Lookup • Join • Move keys

17. Chord Stoica, Morris, Karger, Kaashoek, and Balakrishnan

18. Chord Logical Structure • m-bit ID space (2m IDs), usually m=160. • Think of nodes as organized in a logical ring according to their IDs. N1 N56 N51 N8 N10 N48 N14 N42 N21 N38 N30

19. Consistent Hashing: Assigning Keys to Nodes • Key k is assigned to first node whose ID equals or follows k – successor(k) K54 N1 N56 N51 N8 N10 N48 N14 N42 N21 N38 N30

20. Moving Keys upon Join/Leave • When a node joins, it becomes responsible for some keys previously assigned to its successor • Local change • Assuming load is balanced, how many keys should move? • And what happens when a node leaves?

21. Consistent Hashing Guarantees • For any set of N nodes and K keys, w.h.p.: • Each node is responsible for at most (1 + )K/N keys • When an (N + 1)st node joins or leaves, responsibility for O(K/N) keys changes hands (only to or from the joining or leaving node) • For the scheme described above,  = O(logN) •  can be reduced to an arbitrarily small constant by having each node run (logN) virtual nodes, each with its own identifier

22. Simple Routing Solutions • Each node knows only its successor • Routing around the circle • Good idea? • Each node knows all other nodes • O(1) routing • Cost?

23. Chord Skiplist Routing • Each node has “fingers” to nodes ½ way around the ID space from it, ¼ the way… • finger[i] at n contains successor(n+2i-1) • successor is finger[1] N0 N56 N51 N8 N10 How many entries in the finger table? N48 N14 N42 N21 N38 N30

24. Example: Chord Fingers N0 N10 finger[1..4] N114 N21 finger[5] m entries log N distinct fingers with high probability N30 N90 finger[7] finger[6] N47 N82 N72

25. Chord Data Structures (At Each Node) • Finger table • First finger is successor • Predecessor

26. Forwarding Queries • Query for key k is forwarded to finger with highest ID not exceeding k Lookup( K54 ) K54 N0 N56 N51 N8 N10 N48 N14 N42 N21 N38 N30

27. Remote Procedure Call (RPC) How long does it take?

28. Routing Time • Node n looks up a key stored at node p • p is in n’s ith interval: p  ((n+2i-1)mod 2m, (n+2i)mod 2m] • n contacts f=finger[i] • The interval is not empty (because p is in it) so:f  ((n+2i-1)mod 2m, (n+2i)mod 2m] • RPC f • f is at least 2i-1 away from n • p is at most 2i-1 away from f • The distance is halved: maximum m steps

29. Routing Time Refined • Assuming uniform node distribution around the circle, the number of nodes in the search space is halved at each step: • Expected number of steps: log N • Note that: • m = 160 • For 1,000,000 nodes, log N = 20

30. What About Network Distance? Haifa K54 Lookup( K54 ) N0 N56 China N51 N8 N10 N48 N14 N42 Texas N21 N38 N30

31. Joining Chord • Goals? • Required steps: • Find your successor • Initialize finger table and predecessor • Notify other nodes that need to change their finger table and predecessor pointer • O(log2N) • Learn the keys that you are responsible for; notify others that you assume control over them

32. Join Algorithm: Take II • Observation: for correctness, successors suffice • Fingers only needed for performance • Upon join, update successor only • Periodically, • Check that successors and predecessors are consistent • Fix fingers

33. Creation and Join

35. Join Example joiner finds successor stabilize fixes successor gets keys stabilize fixes predecessor

36. Join Stabilization Guarantee • If any sequence of join operations is executed interleaved with stabilizations, • Then at some time after the last join • The successor pointers form a cycle on all the nodes in the network • Model assumptions?

37. Performance with Concurrent Joins • Assume a stable network with N nodes with correct finger pointers • Now, another set of up to N nodes joins the network, • And all successor pointers (but perhaps not all finger pointers) are correct, • Then lookups still take O(logN) time w.h.p. • Model assumptions?

38. Failure Handling • Periodically fixing fingers • List of r successors instead of one successor • Periodically probing predecessors:

39. Failure Detection • Each node has a local failure detectormodule • Uses periodic probes and timeouts to check liveness of successors and fingers • If the probed node does not respond by a designated timeout, it is suspected to be faulty • A node that suspects its successor (finger) finds a new successor (finger) • False suspicion- the suspected node is not faulty • Suspected due to communication problems

40. The Model? • Reliable messages among correct nodes • No network partitions • Node failures can be accurately detected! • No false suspicions • Properties hold as long as failure is bounded: • Assume a list of r = (logN) successors • Start from stable state and then each node fails with prob. 1/2 • Then w.h.p. find successor returns the closest living successor to the query key • And the expected time to execute find successor is O(logN)

41. What Can Partitions Do? Suspect successor N0 N56 N51 N8 N10 N48 N14 N42 N21 N38 N30 Suspect successor Suspect successor

42. What About Moving Keys? • Left up to the application • Solution: keep soft state, refreshed periodically • Every refresh operation performs lookup(key) before storing the key in the right place • How can we increase reliability for the time between failure and refresh?

43. Summary: DHT Advantages • Peer-to-peer: no centralized control or infrastructure • Scalability: O(log N) routing, routing tables, join time • Load-balancing • Overlay robustness

44. DHT Disadvantages • No control where data is stored • In practice, organizations want: • Content Locality – explicitly place data where we want (inside the organization) • Path Locality – guarantee that local traffic (a user in the organization looks for a file of the organization) remains local • No prefix search