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Computer Science
Posted 6 months ago
Precedence graph algorithm can be used to find out whether the given concurrent schedule is conflict serializable or not. (Check for Conflict Serializablity using Precedence Graph) Assume a schedule S. For S, we construct a graph known as precedence graph. This graph has a pair G = (V,E), where V consists a set of vertices, and E consists a set of edges. The set of vertices is used to contain all the transactions participating in the schedule. The set of edges is used to contain all edges Ti - > Tj for which one of the three conditions holds: Create a node Ti - > Tj if Ti executes write (Q) before Tj executes read (Q). Create a node Ti - Tj if Ti executes read (Q) before Tj executes write (Q). Create a node Ti - > Tj if Ti executes write (Q) before Tj executes write (Q).
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Answer from Sia
Posted 6 months ago
To determine if a given concurrent schedule is conflict serializable using the Precedence Graph algorithm, you follow these steps:
First, identify all the transactions in the schedule and create a vertex in the graph for each transaction. These vertices form the set V in the graph G = (V, E)
Next, examine the operations in the schedule to find conflicts. A conflict occurs when two operations, belonging to different transactions, access the same data item Q, and at least one of those operations is a write
For each conflict, create a directed edge from the vertex representing the transaction that executed its operation first to the vertex representing the transaction that executed its operation second. This forms the set E of edges in the graph
Create an edge Ti → Tj if transaction Ti executes write(Q) before transaction Tj executes read(Q)
Create an edge Ti → Tj if transaction Ti executes read(Q) before transaction Tj executes write(Q)
Create an edge Ti → Tj if transaction Ti executes write(Q) before transaction Tj executes write(Q)
After constructing the graph with vertices and edges, check for cycles. If the graph contains no cycles, the schedule is conflict serializable, as it indicates that the transactions can be serialized without conflict
If the graph does contain a cycle, the schedule is not conflict serializable, as the cycle indicates a circular dependency between transactions that cannot be resolved
In summary, if the precedence graph for schedule S is acyclic, then S is conflict serializable. If the graph contains a cycle, S is not conflict serializable.

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