Precedence Graph for Testing Conflict Serializability in DBMS

Conflict serializability orders any conflicting operations in the same way as some serial execution. A pair of operations is said to conflict if they operate on the same data item and one of them is a write operation.

That means,

• Readi(x) readj(x) - non conflict read-read operation

• Readi(x) writej(x) - conflict read-write operation.

• Writei(x) readj(x) - conflict write-read operation.

• Writei(x) writej(x) - conflict write-write operation.

Where, I and j denote two different transactions Ti and Tj.

Precedence graph

Now consider a precedence graph for testing conflict serializability. It is used to check conflict serializability.

Steps for precedence graph

• For each transaction T, put a node or vertex in the graph.

• For each conflicting pair, put an edge from Ti to Tj.

• If there is a cycle in the graph then schedule is not conflict serializable else schedule is conflict serializable.

Let us consider some examples.

Example 1

Cycle is present so it is not conflict serializable.

Example 2

Cycle is not present, so it is conflict serializable.

Example 3

Cycle is not present, so it is conflict serializable.