Conflict Serializable Schedule: A schedule is called conflict serializable if it can be transformed into a serial schedule by swapping non-conflicting operations. The serial schedule of the Conflict Serializable Schedule can be found by applying topological Sorting on the Precedence Graph of the Conflict Serializable Schedule.
Approach: Follow to below steps to find topological sorting of Precedence Graph:
- Find the indegree of all nodes for the given Precedence Graph and store it in an auxiliary array.
- Now For each node having indegree 0 perform the following:
- Print the current node T as the order of the topological sort.
- Let the node T be the node with in-degree 0.
- Remove T and all edges connecting to T from the graph.
- Update indegree of all nodes after the above steps.
- After the above steps, the topological sort of the given precedence graph can be calculated.
Below is the illustration of the above approach:
Let, the Conflict Serial Schedule be S: R2(A) W2(A) R3(C) W2(B) W3(A) W3(C) R1(A) R2(B) W1(A) W2(B)
- Here node T2 has indegree 0.
- So, select T2 and remove T2 and all edges connecting from it.
- Now T3 has indegree 0. So, select T3 and remove the edge T3→T1.
- At the end select T3. So the topological Sorting is T2, T3, T1.
- Hence, the equivalent serial schedule of given conflict serializable schedule is T2→T3→T1, i.e., S2: R2(A) W2(A) W2(B) R3(C) W3(A) W3(C) R1(A) R2(B) W1(A) W1(B).
There may be more than one equivalent serial schedule of the conflict serializable schedule.
Below is the implementation to get the Serial Schedule of CSS using Topological Sorting:
Equivalent Serial Schedule is :T2 T3 T1
Time Complexity: O(N)
Auxiliary Space: O(N)
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