1. Conflict-Serializability Bharath Kumar Manur Venkataramana Class ID No:- 110

2. Conflicts  What do you mean by a conflict in database?  Example situation for such a conflict? Online Reservation Systems.  4 situations where conflict cannot happen 1) Ri (X) ; Rj (Y) will never conflict, even if database element X=Y. 2) Ri (X) ; Wi (Y) will not conflict for X not equal to Y. 3) Wi (X) ; Rj (Y) will not conflict for X not equal to Y. 4) Wi (X) ; Wj (Y) will not conflict for X not equal to Y.

3. Conflicts  There are 3 situations where we may not swap the order of actions. They are:- 1) Two actions of the same transactions conflict. 2) Two writes of the same database element by different transactions conflict. 3) A read and a write of the same database element by different transactions also conflict.

4. Conflict Serializability  Two actions conflict if:- 1) They are issued by different transactions. 2) They operate on the same database element. 3) At least one of them is a write operation.  The 2 schedules S and S 1 are conflict-equivalent, if S can be transformed into S 1 by a sequence of non-conflicting swaps of adjacent actions.  A schedule is conflict-serializable if it is conflict-equivalent to a serial schedule.

5. Conflict Serializability (Contd.)‏  Schedule 1 can be transformed into Schedule 5, a serial schedule where T 2 follows T 1, by series of swaps of non-conflicting instructions.  Therefore Schedule 1 is conflict serializable. Schedule 1Schedule 5

6. Precedence Graphs  A Precedence graph is used to find out whether a schedule is conflict-serializable or not.  There are 2 types of precedence graphs :-  Acyclic Graphs which determines that the Schedule S is conflict-serializable.  Cyclic Graphs which are nothing but the conflict graphs which cannot determine the precedence order for the Schedule S.

7. Algorithm to produce a Precedence Graph  Add a node for each transaction.  Add a directed edge from Ti to Tj, if Tj reads the value of a database element written by Ti.  Add a directed edge from Ti to Tj, if Tj writes a value into the database element after it has been read by Ti.  If the graph is cyclic, then the Schedule is not Conflict- Serializable.

8. Acyclic Graphs  An example of a Schedule S. Example Schedule R 2 (a) R 1 (b) W 2 (a) R 3 (a) W 1 (b) W 3 (a) R 2 (b) W 2 (b) T3T1T2 Precedence Graph

9. Conflict or Cyclic Graphs  An example of a Schedule S. Example Schedule W 1 (a) R 2 (a) R 3 (b) W 2 (c) R 3 (c) W 3 (a) W 3 (b) R 1 (b) Precedence Graph T1T2 T3 Execution is conflict-serializable only if the conflict graph is acyclic.

10. Test for Conflict-Serializability  Let S be a schedule which consists of action of n transactions, T1 -> T2 -> T3 ->..... -> Tn -> T1.  The actions of T1 precedes T2 and so on till Tn, but since the action of Tn precedes T1.  Due to Tn -> T1, we find there is a cycle in the precedence graph and the conclusion is that the schedule is not conflict-serializable.  Finally a schedule is conflict serializable if and only if its precedence graph is acyclic.