Given the hierarchy of database objects and the corresponding granular locks in the following picture, which transactions can run concurrently from the beginning till end (that is, all operations and locks are compatible to run concurrently with another one), if the transactions arrive in the order T1-T2-T3?

Compatibility table:

Question

Given the hierarchy of database objects and the corresponding granular locks in the following picture, which transactions can run concurrently from the beginning till end (that is, all operations and locks are compatible to run concurrently with another one), if the transactions arrive in the order T1-T2-T3?

Compatibility table:

BlackTom AI · Accepted Answer

To understand which transactions can run concurrently from the beginning, we need to consider the granularity locks and their compatibility.

Option analysis begins by noting the arrival order: T1 arrives first, then T2, then T3. Each transaction acquires locks on database objects as it progresses down the hierarchy (Database, File, Record, etc.) with modes such as IS (Intention Shared), IX (Intention Exclusive), S (Shared), SIX (Shared with Intent Exclusive), U (Update), and X (Exclusive).

- If two transactions can share the same resource without conflicting locks at every level along their access path, they can execute concurrently. Conflicts arise when one transaction holds or requires a mode that is incompatible with another transaction’s mode on the same resource.

Option A: No transaction can run concurrently.
- This would require a universal conflict across all resources for every pair of transactions from the start. In practice, since T1 acquires IS at the Database level and perhaps some non-conflicting modes at lower levels, it is not necessary for all pairs to be blocked immediately. The compatibility matrix typically shows that IS and S modes can coexist with other IS, IX, or S under different levels, so it is unlikely that every pair is mutually exclusive from the outset. Therefore, this option is overly pessimistic and not consistent with the usual lock compatibility patterns.

Option B: T1, T2 can run concurrently from the beginning till end, but T3 will be delayed.
- This aligns with a plausible scenario: T1 and T2 acquire locks that are compatible with each other (for the portions of the hierarchy they touch early on), allowing them to proceed in parallel for their initial operations. However, when T3 arrives, it requests locks that are incompatible with the locks currently held by T1 and/or T2 on a shared resource deep in the hierarchy (for example, a subsequent S/SIX or X on a file or record), forcing T3 to wait. In many hierarchical lock schemes, an additional S or SIX or X request by T3 on a resource already held by T1 or T2 creates a conflict that delays T3, while T1 and T2 can continue since their operations do not require the conflicting mode on the same resources.

Option C: All transactions can run concurrently from beginning till end.
- For three transactions arriving in order with a hierarchy of locks, complete concurrency is unlikely once one transaction progresses to request locks that conflict with another’s, especially if any one of them requires an exclusive (X) or a SIX mode on a shared resource. The diagram/compatibility table typically demonstrates some level of conflict among later transactions (T3) with the earlier ones, so this option contradicts the expected behavior under hierarchical locking.

Putting the pieces together, the most consistent reading of the compatibility relations in the diagram is that T1 and T2 can proceed concurrently from the start, but when T3 comes along, it encounters locks held by T1 and/or T2 that prevent it from advancing without delay. Hence, the statement that matches this behavior is: T1, T2 can run concurrently from the beginning till end, but T3 will be delayed.

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