Conflict-Serializability (section 18.2 of Concurrency Control)

1. Conflict-Serializability (section 18.2 of Concurrency Control) - Amith KC Student ID – 006498310

2. Overview • One of the sufficient conditions to assure that a schedule is serializable is “conflict-serializability”. • Idea of Conflicts. • Conflicting and non-conflicting actions. • Conflict-equivalent and conflict-serializability schedules. • Precedence Graphs • Definition. • Test for conflict-serializability.

3. Conflicts • Definition • is a pair of consecutive actions in a schedule such that, if their order is interchanged, then the behavior of at least one of the transactions involved can change. • Non-conflicting actions: Let Ti and Tjbe two different transactions (i ≠ j), then: • ri(X); rj(Y) is never a conflict, even if X = Y. The reason is that neither of thesesteps change the value of any database element. • ri(X); wj(Y) is not a conflict provided X ≠ Y. • wi(X); rj(Y) is not a conflict provided X ≠ Y. • Similarly, wi(X); wj(Y) is also not a conflict, provided X ≠ Y.

4. continued… • Three situations of conflicting actions (where we may not swap their order) • Two actions of the same transaction. • e.g., ri(X);wi(Y) • Two writes of the same database element by different transactions. • e.g., wi(X);wj(X) • A read and a write of the same database element by different transactions. • e.g., ri(X);wj(X) • To summarize, any two actions of different transactions may be swapped unless: • They involve the same database element, and • At least one of them is a write operation.

5. continued… • Conflict-equivalent schedules: • Two schedules are called conflict-equivalent schedules if they can be turned one into the other by a sequence of non-conflicting swaps of adjacent actions. • Conflict-serializability schedule: • A schedule is conflict-serializable if it is conflict-equivalent to a serial schedule. Conflict Serializability is not required for a schedule to be serializable, but it is the condition that the schedulers in commercial systems generally use when they need to guarantee serializablity.

6. Precedence Graphs • Conflicting pairs of actions (of a schedule S) put constraints on the order of transactions in the hypothetical, conflict-equivalent serial schedule. • For a schedule S, involving transactions T1 and T2(among other transactions), we say that T1 takes precedence over T2 (written as T1 <s T2)if there are actions A1 of T1 and A2 of T2, such that: • A1 is ahead of A2 in S, • Both A1 and A2 involve the same database element, and • At least one of them is a write operation.

7. continued… • The precedences mentioned in the previous slide can be depicted in a “precedence graph”. • The nodes in this graph are the transactions of the schedule S. • Example of a precedence graph: • Consider a schedule S which involves three transactions T1, T2 and T3, i.e., S: r2(A); r1(B); w2(A); r3(A); w1(B); w3(A); r2(B); w2(B); The precedence graph for this as is shown below: 1 2 3 Figure 1

8. Test for conflict-serializability • Construct the precedence graph for S and observe if there are any cycles. • If yes, then S is not conflict-serializable • Else, it is a conflict-serializable schedule. • Example of a cyclic precedence graph: • Consider the below schedule S1: r2(A); r1(B); w2(A); r2(B); r3(A); w1(B); w3(A); w2(B); The precedence graph for this as shown below: 1 2 3 Figure 2

9. continued… • Observing the actions of A in the previous example (figure 2), we can find that T2 <s1 T3. • But when we observe B, we get both T1 <s1 T2 and T2 <s1 T1. Thus the graph has a cycle between 1 and 2. So, based on this fact we can conclude that S1 is not conflict-serializable.

10. Why the Precedence-Graph test works • A cycle in the graph puts too many constraints on the order of transactions in a hypothetical conflict-equivalent serial schedule. • If there is a cycle involving n transactions T1 T2 ..Tn T1 • Then in the hypothetical serial order, the actions of T1 must precede those of T2 which would precede those of T3... up to n. • But actions of Tn are also required to precede those of T1. • So, if there is a cycle in the graph, then we can conclude that the schedule is not conflict-serializable.

11. Thank you!