Precedence graph
A precedence graph, also named conflict graph and serializability graph, is used in the context of concurrency control in databases.
The precedence graph for a schedule S contains:
- A node for each committed transaction in S
- An arc from Ti to Tj if an action of Ti precedes and conflicts with one of Tj's actions.
Precedence graph example
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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:-
- For each transaction Ti participating in schedule S, create a node labelled Ti in the precedence graph. So the precedence graph contains T1, T2, T3
- For each case in S where Tj executes a read_item(X) after Ti executes a write_item(X), create an edge (Ti --> Tj) in the precedence graph. Here this process is not happening anywhere as there is no read after write.
- For each case in S where Tj executes a write_item(X) after Ti executes a read_item(X), create an edge (Ti --> Tj) in the precedence graph. This will bring to front a directed graph from T1 to T2.
- For each case in S where Tj executes a write_item(X) after Ti executes a write_item(X), create an edge (Ti --> Tj) in the precedence graph. It creates a directed graph from T2 to T1, T1 to T3, and T2 to T3.
- The schedule S is serializable if and only if the precedence graph has no cycles. As T1 and T2 constitute a cycle, the above schedule is not supposed to be serializable.
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