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Assignment 2 - Solution

Assignment 2 - Solution 1. w 0 [x,y,z ] c 0 r 1 [x] r 2 [y] w 2 [y] r 3 [z] w 3 [z] r 2 [z] w 2 [y] w 1 [z] w 1 [y] c 1 c 2 c 3 a. An equivalent serial history must preserve the order of conflicting operations . So, which operations conflict? We’ll use  to mean

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Assignment 2 - Solution

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  1. Assignment 2 - Solution • 1. w0[x,y,z] c0 r1[x] r2[y] w2[y] r3[z] w3[z] r2[z] w2[y] w1[z] w1[y] c1 c2 c3 • a. An equivalent serial history must preserve the order of conflicting • operations. So, which operations conflict? We’ll use  to mean • “precedes and conflicts with”.w0[x,y,z]  all other reads and writesr2[y] and both w2[y]’s  w1[y]w3[z]  r2[z]r3[x] and w3[z] w1[z] • So, the only equivalent serial history has transactions in the order 0-3-2-1 • b. Since w3[z]  r2[z] and c2 c3 the history is not recoverable. Hence, it • doesn’t avoid cascading aborts and isn’t strict. There are two other • violations of strictness: w3[z] < w1[z] < c3 and w2[y] < w1[y] < c2.

  2. 2. w0[x,y,z] c0 r1[x] r2[y] w2[y] r3[z] r2[z] w2[y] w1[z] w1[y] c1 c2 c3 • (same as (1), except delete w3[z] ) • a. We no longer have w3[z]  r2[z]. So the order of T3 relative to T2 is unconstrained. Therefore, the history is now equivalent to a serial history with transactions in the order 0-3-2-1 or 0-2-3-1. • b. The history is now recoverable and avoids cascading aborts. But it still isn’t strict because w3[z] < w1[z] < c3 and w2[y]  w1[y]  c

  3. 3. w0[x,y,z] c0 r1[x] r2[y] w2[y] r3[z] w3[z] r2[z] w2[y] w1[z] w1[y] c1c3 c2 • (same as (1), except that c2 is moved after c3) • a. This has no effect on serializability, so the answer is the same as 1a.b. This also makes the history recoverable, since w3[z]  r2[z] and c3  c2. But it still doesn’t avoid cascading aborts, because of the same conflict: T2 reads uncommitted data (z) from T3. Obviously, it is not strict.

  4. 4. w0[x,y,z] c0 r1[x] r2[y] w2[x] r3[z] w3[z] r2[z] w2[y] w1[z] w1[y] c1 c2 c3 • (same as (1), except the first w2[y] becomes w2[x]) • a. Now we have r1[x]  w2[x] and w2[y]  w1[y] forming a cycle, so there is no equivalent serial history. • b. w3[z]  r2[z] and c2 c3 is unchanged from (1), so the history is not recoverable since T2 reads uncommitted data.

  5. 5. w0[x,y,z] c0 r1[x] r2[y] w2[y] r3[z] w3[z] r2[z] w2[y] c2 w1[z] w1[y] c1 c3 • (same as (1), except c2 is moved before w1[z])a. This has no effect on serializability • b.It is tempting to think that this helps strictness, since we now have w3[z] < c3 < w1[z] and w2[y] < c2 < w1[y]. But strictness implies avoidance of cascading aborts, which implies recoverability. And we still have the same old violation of recoverability: T2 still reads uncommitted data (z) from T3. So the execution isn’t strict.

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