Efficient Solutions to the Replicated Log and Dictionary Problems

1. Efficient Solutions to the Replicated Log and Dictionary Problems By Gene T J Wuu and Arthur J Bernstein Sunita Gupta, COEN 317, Spring 05

2. Outline • Introduction • The model of the environment • The Log Problem and its Application • The Log Problem • The Dictionary Problem • Efficient Solutions • A New Solution to the Log Problem • A Efficient Solution to the Dictionary Problem • Comparison with other work • Some Applications

3. Introduction • In this paper, authors propose efficient algorithms to maintain a replicated dictionary in an unreliable distributed system using log. • Replicated log is used to achieve mutual consistency of replicated data in an unreliable network.

4. Introduction (cont’) • Data replication In many application, data objects are highly shared & reliability and fast access are very important. • Logs Useful in achieving distributed synchronization and in gathering information about the state of the network

5. The model of the environment • An n node connected Network with nodes N1, N2,.., Nn. • A node id – an integer in [n] denote set {1,2,..n} • Two kinds of operations – the communication operation send and receive, and non communication operations • Events are locally atomic ( i.e. if a node crashes during the execution of an operation, there will be not effect on local data) • Events are distinguished by the time and place at which they occur.

6. The model of the environment(Cont’) • There is local clock at each node • time(e) – time of event e • Node(e) – node at which event e occurred • Op(e) – invoked operations and its parameters • <E, → > a partial ordering relation on E • Partial ordering relation – events occurring at the same node are totally ordered and e1→ e2 – e1 send event and e2 – corresponding receive event

7. The model of the environment(Cont’) • The unreliable behaviors covered by this model – lost messages, broken communication links, network partition, and failed nodes • Message in transmit not allowed to change in arbitrary ways.

8. The Log Problem and its application • Each Node maintains its own view of the log • a distribution algorithm is employed to keep the view up to date.

9. The Log Problem • Problem of finding an algorithm to maintain the log such that, given an execution < E, → >, for every event e, f → e iff fR є L(e)

10. The Log Problem (Cont’) f → e iff fR є L(e) --- P1 • Event f happened before event e iff event record describing event f is propagated to local copy of log of Node(e) immediately after event e completes. • event record – contains operation type, time type and Node Id.

11. The Log Problem (Cont’) • To achieve P1, node exchange messages containing appropriate portion of the log. E.g. • Consider Node N1 and N2 • N1 only sends records to those events which have occurred at N1 since it last sent a message to N2 (updated one) • Cannot achieve P1 – message delivery is not guaranteed.

12. The Log Problem (Cont’) • Trivial solution: • At each non-communication event, e, occurring at Ni, Ni inserts eR into Li, and at each send event Ni includes Li in the message.

13. The Dictionary Problem • Dictionary – an abstraction of data objects (file directory), a data base dictionary, a recourse management table • Two non-communication operations on dictionary x – • delete(x) • insert(x) • For Uniquness of each entry – tag each item to be inserted with time stamp.

14. The Dictionary Problem (Cont’) • Problem of finding an algorithm for maintaining the dictionary such that, given an execution < E, →>, for every event e, x є V(e) iff Cx → e and there does not exist an x-delete event g, such that g → e.

15. The Dictionary Problem (Cont’) x є V(e) iff Cx → e and there does not exist an x-delete event g, such that g → e --- P2 • Dictionary entry x is a part of local copy of dictionary at Node(e) iff the unique event Cx which inserts x happened before event e and there is no x-delete event g before event e occurred.

16. The Dictionary Problem (Cont’) • Obvious solution: • At each event, e, such that node(e) = i, Ni computed V(e) in the following way:

17. Efficient solutions • Problem with previous solution: • Excessive communication cost • Excessive computational cost • Excessive storage cost

18. A New Solution to the Log Problem • 2-Dimension Time Table(2DTT) • Used by each node • Each Node Ni keeps a two-dimensional time-table Ti , which corresponds to Ni's most recent knowledge of the vector clocks. • Can tell how up to date other nodes are about events occurring in the network

19. A New Solution to the Log Problem (Cont’) • Node maintains following information: • A service called clocki – each reference to clocki returns an integer number greater than that returned by the last reference. • 2-Dimension time table Ti – Each time-table ensures the following time- table property • Ti[k, u] = t, Ni node knows that Nk node has received the records of all events which have occurred at Nu up to t.

20. A New Solution to the Log Problem (Cont’) • To reduce communication it is desirable for a Node to know which node have received the record of a particular event. To this end a predicate HasRec, is defined as follows : HasRec(Ti;eR;k) = Ti[k;eR.node] >= eR.time. where if hasrec function is true at Ni then Nk has learned about event e. • The protocol ensures that whenever a site is aware of an event (insert or delete in the dictionary), it is aware of all causally proceeding events.

21. An efficient Solution to the Dictionary Problem • Developed to overcome excessive computational costs and excessive storage cost • Each node separately maintains its view of the dictionary as well as partial log which records some events which have happened in the network. • Only partial log is kept at each node.

22. An efficient Solution to the Dictionary Problem (Cont’) • If the communication link between two node breaks or message is lost, node can still learn indirectly, of a new event using information passed through other nodes. • We assume that the state of node is maintained in stable storage and data is not lost when a crash occurs.

23. Comparison with Other Work 1. Fishers and Michael – Solution requires a node to send its entire copy of the dictionary in each message. Solution is expensive. 2. 1- dimension time table – Each node maintains synchronization set and node sends event record to other node even though node learnt about the event. Thus SS grows unboundedly.

24. Comparison with Other Work • 2-DTT – Deficient of approach - it is sent as a part of message => has size O(n^2) excessive storage and communication overhead. • Modified algorithm: • Each node stores the complete 2DTT but sends only its own row. • Each node stores only its own row and a row for each of its neighbors; it sends only those rows which correspond to neighbors of the target node. • Each node stores only its neighbors rows and neighbors columns; it sends only those rows to node which correspond to neighbors of that node.

25. Some applications uses Log solution • Replicated numeric data with add-to and subtract-from operations. • Detection of failure – Log is used to collect records of communication events occuring in the network.

26. References • Partial Database Replication using Epidemic Communication by J Holliday, D Agrawal, A Abbadi • Class Notes