Conflict Serializable Schedule

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A conflict serializable schedule is a concept used in database management systems to ensure the correctness and consistency of concurrent transactions. It is a property of schedules that guarantees the same final result as if the transactions had been executed serially, one after the other, in some order.

A schedule in the context of database transactions refers to the order in which the individual operations of different transactions are executed. Transactions may consist of multiple operations such as read (R) and write (W) operations on database objects.

To determine whether a schedule is conflict serializable, we need to consider the dependencies among transactions. A dependency exists between two operations if they refer to the same database object, and at least one of them is a write operation. There are two types of dependencies:

  1. Read-Write (RW) Dependency: A read operation depends on a previous write operation on the same database object. The read operation must read the value written by the write operation.
  2. Write-Write (WW) Dependency: A write operation depends on a previous write operation on the same database object. The write operation must overwrite the value written by the previous write operation.

A schedule is conflict serializable if it is equivalent to some serial schedule that maintains the order of all conflicting operations. In other words, if we can reorder the operations in the schedule while preserving the order of conflicting operations, it is conflict serializable.

One common method to determine conflict serializability is by constructing a precedence graph. The precedence graph represents the dependencies between transactions in the schedule. If the graph does not contain any cycles, the schedule is conflict serializable. If a cycle exists, the schedule is not conflict serializable.

To construct a precedence graph, follow these steps:

  1. Create a node for each transaction involved in the schedule.
  2. For each pair of conflicting operations (Ri, Wj) or (Wi, Wj) in the schedule, draw an edge from the transaction of the earlier operation to the transaction of the later operation.

If the resulting graph contains no cycles, the schedule is conflict serializable. If a cycle exists, the schedule is not conflict serializable.

By analyzing the precedence graph, you can identify the potential conflicts and determine whether the schedule is conflict serializable.

Conflicting Operations:

Conflicting operations in the context of database transactions are operations that access or modify the same data item and may lead to inconsistent results if executed concurrently. There are two types of conflicting operations:

  1. Read-Write (RW) Conflict:
    • Occurs when one transaction reads a data item that another transaction has modified or is in the process of modifying.
    • The first transaction reads the value after the modification by the second transaction.
    • If the first transaction had read the value before the modification, it would have obtained a different result.
  2. Write-Write (WW) Conflict:
    • Occurs when two transactions write to the same data item.
    • The order of the write operations affects the final value of the data item.
    • If the second transaction overwrites the value written by the first transaction, the final value will be different from what it would have been if the operations were executed serially.

Conflicting operations are important to consider when analyzing the concurrency control and correctness of a schedule. To ensure the consistency of data and prevent conflicts, database management systems use various techniques such as locking, timestamp ordering, and optimistic concurrency control. These techniques help manage concurrent transactions and guarantee the correctness of the final results.

Example of Conflicting Operations:

Sure! Let’s consider a simple example with two transactions: Transaction T1 and Transaction T2. Assume we have a database table named “Accounts” with two columns: “Account Number” and “Balance”.

Here are the operations performed by each transaction:

Transaction T1:

  1. T1 reads the current balance of Account A.
  2. T1 deducts $100 from the balance of Account A.
  3. T1 writes the updated balance back to Account A.

Transaction T2:

  1. T2 reads the current balance of Account A.
  2. T2 adds $50 to the balance of Account A.
  3. T2 writes the updated balance back to Account A.

In this example, there are conflicting operations between T1 and T2 because they both read and write to the same data item (the balance of Account A). Let’s identify the conflicts:

  1. Read-Write (RW) Conflict:
    • T1 reads the balance of Account A (Read operation).
    • T2 reads the balance of Account A (Read operation).
    • T2 writes the updated balance to Account A (Write operation).
  2. Write-Write (WW) Conflict:
    • T1 writes the updated balance to Account A (Write operation).
    • T2 writes the updated balance to Account A (Write operation).

These conflicting operations can lead to inconsistent results if executed concurrently without proper coordination or concurrency control mechanisms in place.

For example, if T1 and T2 are executed concurrently without any coordination, the final balance of Account A will depend on the order of execution of their write operations. If T2’s write operation executes before T1’s write operation, the final balance will be different compared to the case where T1’s write operation executes before T2’s write operation.

Proper concurrency control techniques like locking or timestamp ordering can be used to handle these conflicts and ensure a consistent and correct final result.

Conflict Equivalent:

Conflict equivalence is a concept used to determine whether two schedules are equivalent in terms of their outcome, despite having different execution orders. Two schedules are said to be conflict equivalent if they have the same read and write dependencies and, as a result, produce the same final results or final database state.

To determine conflict equivalence between two schedules, we need to compare their dependencies. Here are the steps to check conflict equivalence:

  1. Identify the read and write operations in both schedules.
  2. For each read operation in a schedule, identify the write operation it depends on. Similarly, for each write operation, identify the write operation it depends on.
  3. Compare the dependencies of the read and write operations in both schedules.

    a. If the sets of read and write dependencies are the same in both schedules, they are conflict equivalent.

    b. If the sets of dependencies differ, the schedules are not conflict equivalent.

For example, let’s consider two schedules, Schedule A and Schedule B:

Schedule A:

  1. T1 writes X
  2. T2 reads X
  3. T1 writes Y
  4. T2 reads Y

Schedule B:

  1. T2 reads X
  2. T1 writes X
  3. T2 reads Y
  4. T1 writes Y

To check conflict equivalence, we analyze the dependencies:

Schedule A:

  • Read operation in Step 2 depends on Write operation in Step 1 (RW dependency).
  • Read operation in Step 4 depends on Write operation in Step 3 (RW dependency).

Schedule B:

  • Read operation in Step 1 depends on Write operation in Step 2 (RW dependency).
  • Read operation in Step 3 depends on Write operation in Step 4 (RW dependency).

Comparing the dependencies, we can see that both schedules have the same read and write dependencies, and therefore they are conflict equivalent.

Conflict equivalence is important in concurrency control and transaction management to ensure that different schedules produce consistent results, regardless of their execution order.

Example of Conflict Equivalent:

Let’s consider two schedules, Schedule A and Schedule B, involving two transactions: Transaction T1 and Transaction T2. Assume we have a database table named “Employees” with columns “Employee ID” and “Salary.”

Schedule A:

  1. T1 reads the salary of Employee E1.
  2. T2 reads the salary of Employee E2.
  3. T1 writes a new salary for Employee E1.
  4. T2 writes a new salary for Employee E2.

Schedule B:

  1. T2 reads the salary of Employee E2.
  2. T1 reads the salary of Employee E1.
  3. T2 writes a new salary for Employee E2.
  4. T1 writes a new salary for Employee E1.

To determine if these schedules are conflict equivalent, we need to analyze their dependencies:

Schedule A:

  • Read operation in Step 1 depends on no write operations.
  • Read operation in Step 2 depends on no write operations.
  • Write operation in Step 3 depends on no read or write operations.
  • Write operation in Step 4 depends on no read or write operations.

Schedule B:

  • Read operation in Step 1 depends on no write operations.
  • Read operation in Step 2 depends on no write operations.
  • Write operation in Step 3 depends on no read or write operations.
  • Write operation in Step 4 depends on no read or write operations.

Both schedules have no dependencies between their read and write operations. Therefore, they are conflict equivalent since they produce the same final database state regardless of the order of execution.

In this example, even though the execution order of the read and write operations differs between Schedule A and Schedule B, they are conflict equivalent because the read and write operations do not conflict with each other. Consequently, both schedules will result in the same final state of the “Employees” table.