A schedule of three database transactions \(T_1\), \(T_2\), and \(T_3\) is shown. \(R_i(A)\) and \(W_i(A)\) denote read and write of data item A by transaction \(T_i\), \(i = 1, 2, 3\). The transaction \(T_1\) aborts at the end. Which other transaction(s) will be required to be rolled back?
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In transaction management, when one transaction writes to a data item and another transaction reads or writes the same item, the abort of the first transaction often causes the second transaction to be rolled back. Always check for read-write dependencies.
In the given transaction schedule, transaction \( T_1 \) writes to data item \( Y \) and then aborts. Since \( T_1 \) aborts, any transaction that has read or written data modified by \( T_1 \) must be rolled back to maintain the consistency of the database.
Let’s analyze the transactions:
- Transaction \( T_1 \) writes to \( Y \) (i.e., \( W_1(Y) \)).
- Transaction \( T_2 \) reads \( Y \) (i.e., \( R_2(Y) \)).
- Transaction \( T_3 \) also reads \( Y \) (i.e., \( R_3(Y) \)).
Since both \( T_2 \) and \( T_3 \) read \( Y \), which was modified by \( T_1 \), they will be impacted by the abort of \( T_1 \). As a result, both \( T_2 \) and \( T_3 \) must be rolled back to preserve the consistency of the database.
Therefore, the correct answer is (C) Both \( T_2 \) and \( T_3 \).
