Suppose that transactions T1 and T2 can be decomposed into the subtransactions T1 : T1,1, T1,2 and T2 : T2,1, T2,2 such that the database items accessed by T1,1 and T2,1 are disjoint from the items accessed by T1,2 and T2,2. Instead of guaranteeing that all schedules involving T1 and T2 are serializable, suppose that a concurrency control guarantees that T1,1 is always executed serializably with T2,1 and that T1,2 is always executed serializably with T2,2.

a. Will T1 always be serializable with T2? Explain.
b. What minimal additional condition on the subtransactions guarantees that the effect of executing T1 concurrently with T2 is the same as a serial schedule?
c. Assuming that the condition of (b) holds, what advantage does the new concurrency control have over a concurrency control that guarantees serializability?

a. No. T1,1 might be serialized before T2,1, and T1,2 might be serialized after T2,2.
Thus there is no equivalent serial order.
b. One condition is that T1,1 commutes with T2,1 and thus they can be serialized in
either order.
c. Locks acquired by T1,1 or T2,1 are released early.