Precedence graph

Precedence graph example

Example 1:

or

Example 2:

A precedence graph of the schedule D, with 3 transactions. As there is a cycle (of length 2; with two edges) through the committed transactions T1 and T2, this schedule (history) is not Conflict serializable.

Testing Serializability with Precedence Graph

The drawing sequence for the precedence graph:-

1. For each transaction T_i participating in schedule S, create a node labelled T_i in the precedence graph. So the precedence graph contains T₁, T₂, T₃
2. For each case in S where T_i executes a write_item(X) then T_j executes a read_item(X), create an edge (T_i --> T_j) in the precedence graph. This occurs nowhere in the above example, as there is no read after write.
3. For each case in S where T_i executes a read_item(X) then T_j executes a write_item(X), create an edge (T_i --> T_j) in the precedence graph. This results in a directed edge from T₁ to T₂.
4. For each case in S where T_i executes a write_item(X) then T_j executes a write_item(X), create an edge (T_i --> T_j) in the precedence graph. This results in directed edges from T₂ to T₁, T₁ to T₃, and T₂ to T₃.
5. The schedule S is conflict serializable if the precedence graph has no cycles. As T₁ and T₂ constitute a cycle, then we cannot declare S as serializable or not and serializability has to be checked using other methods.