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

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.

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 T i and T j be two different transactions (i ≠ j), then: –r i (X); r j (Y) is never a conflict, even if X = Y. The reason is that neither of these steps change the value of any database element. –r i (X); w j (Y) is not a conflict provided X ≠ Y. –w i (X); r j (Y) is not a conflict provided X ≠ Y. –Similarly, w i (X); w j (Y) is also not a conflict, provided X ≠ Y.

continued… Three situations of conflicting actions (where we may not swap their order) –Two actions of the same transaction. e.g., r i (X);w i (Y) –Two writes of the same database element by different transactions. e.g., w i (X);w j (X) –A read and a write of the same database element by different transactions. e.g., r i (X);w j (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.

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. continued…

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 T 1 and T 2 (among other transactions), we say that T 1 takes precedence over T 2 (written as T 1 < s T 2 )if there are actions A 1 of T 1 and A 2 of T 2, such that: –A 1 is ahead of A 2 in S, –Both A 1 and A 2 involve the same database element, and –At least one of them is a write operation.

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 T 1, T 2 and T 3, i.e., S: r 2 (A); r 1 (B); w 2 (A); r 3 (A); w 1 (B); w 3 (A); r 2 (B); w 2 (B); The precedence graph for this as is shown below: Figure 1

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 S 1 : r 2 (A); r 1 (B); w 2 (A); r 2 (B); r 3 (A); w 1 (B); w 3 (A); w 2 (B); The precedence graph for this as shown below: Figure 2

continued… Observing the actions of A in the previous example (figure 2), we can find that T 2 <s 1 T 3. But when we observe B, we get both T 1 <s 1 T 2 and T 2 <s 1 T 1. Thus the graph has a cycle between 1 and 2. So, based on this fact we can conclude that S 1 is not conflict-serializable.

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 T 1 T 2..T n T 1 –Then in the hypothetical serial order, the actions of T 1 must precede those of T 2 which would precede those of T 3... up to n. –But actions of T n are also required to precede those of T 1. –So, if there is a cycle in the graph, then we can conclude that the schedule is not conflict-serializable.

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