CP5520 - Advanced Databases and Applications Assignment, James Cook University, Australia

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1. Transaction Processing -

Consider schedules S₁ and S₂ below.

S₁: r₂(X), r₂(Z), r₃(Y), w₂(X), w₂(Z), w₃(Y), r₁(Z), r₃(X), w₃(X), r₁(X), r₃(Z), w₁(X), w₃(Z), w₁(Z)

S₂: r₁(X), r₁(Z), r₂(Y), w₂(Y), w₁(X), r₃(Y), w₁(Z), r₂(X), r₃(X), r₂(Z), w₂(Z), r₃(Z), w₃(Y), w₃(Z)

(a) Apply the basic timestamp ordering (BTO) algorithm to schedules S₁ and S₂. Determine whether or not the algorithm allows the execution of the schedules, and discuss cascading rollback (if any).

Answer -

Schedule 1 -

1) First of all, we will calculate the read and write time stamp of the data items X, Y, Z.

The time stamp of transactions T₁, T₂, T₃ is 7, 1, 3 as the first operation of these transactions is issued on these timestamps.

To find Read time stamp of X, Y, Z

Read timestamp is the largest time stamp when a transaction successfully completes read operation.

R_TS(X)=7 as transaction T₁ successfully completed read operation on it.

R_TS(Y)=3 as transaction T₃ successfully completed read operation on it.

R_TS(Z)=7 as transaction T₁ successfully completed read operation on it.

Write timestamp is the largest time stamp when a transaction successfully completes read operation.

W_TS(X)=7 as transaction T₁ successfully completed write operation on it.

W_TS(Y)=3 as transaction T₃ successfully completed write operation on it.

W_TS(Z)=7 as transaction T₁ successfully completed write operation on it.

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2) Now, we will apply basic time stamp ordering protocol which says

if TS_(T) issues W_TS(A) then, it checks 2 conditions

i) If R_TS(A)>TS(T) or W_TS(A)>TS(T) then, abort and rollback T and reject write operation

ii) Otherwise, execute Write operation and update W_TS(A)=TS(T)

if TS_(T) issues R_TS(A) then, it checks 2 conditions

iii) If W_TS(A)>TS(T) then, abort and rollback T and reject write operation

iv) Otherwise, execute read operation and update R_TS(A)=Max(TS(T),current R_TS(A)).

a) Now, in this schedule transaction T₂ issues read operation on data item X

W_TS(X)=7, TS(T2)=1 . Since, W_TS(X)> TS(T2) so, this read operation is aborted.

b) Now, transaction T₂ issues read operation on data item Z

W_TS(Z)=7, TS(T2)=1 . Since, W_TS(X)> TS(T2) so, this read operation is aborted.

c) Now, transaction T₃ issues read operation on data item Y

W_TS(Y)=3, TS(T3)=3 . Since, W_TS(X)=TS(T3) so, this read operation is executed.

R_TS(Y)=3

d) Now, transaction T₂ issues write operation on data item X

W_TS(X)=7, TS(T2)=1 and. R_TS(X)=7, TS(T2)=1 Since, W_TS(X)>TS(T2) and also R_TS(X)>TS(T2) so, this write operation is aborted

e) Now, transaction T₂ issues write operation on data item Z

W_TS(Z)=7, TS(T2)=1 and. R_TS(Z)=7, TS(T2)=1 Since, W_TS(Z)>TS(T2) and also R_TS(Z)>TS(T2) so, this write operation is aborted

f) Now, transaction T₃ issues write operation on data item Y

W_TS(Y)=3, TS(T3)=1 and. R_TS(X)=3, TS(T3)=1 Since, W_TS(Y)>TS(T3) and also R_TS(Y)>TS(T3) so, this write operation is aborted

g) T₁ issues read operation on data item Z

W_TS(Z)=7, TS(T1)=7.. Since, W_TS(Z)=TS(T1) so, this read operation is executed and R_TS(Z)=7.

h) Now, transaction T₃ issues read operation on data item X

W_TS(X)=7, TS(T3)=3 . Since, W_TS(X)>TS(T3) so, this read operation is aborted.

i) Now, transaction T₃ issues write operation on data item X

W_TS(X)=7, TS(T3)=3 and. R_TS(X)=7, TS(T3)=3 Since, W_TS(X)>TS(T3) and also R_TS(X)>TS(T3) so, this write operation is aborted

j) T₁ issues read operation on data item X

W_TS(X)=7, TS(T1)=7.. Since, W_TS(X)=TS(T1) so, this read operation is executed and R_TS(X)=7.

k) T₃ issues read operation on data item Z

W_TS(Z)=7, TS(T3)=3.. Since, W_TS(Z)>TS(T3) so, this read operation is aborted.

l) Now, transaction T₁ issues write operation on data item X

W_TS(X)=7, TS(T1)=7 and. R_TS(X)=7, TS(T3)=7 Since, W_TS(X)=TS(T3) and also R_TS(X)=TS(T3) so, this write operation is executed and W_TS(X)=7

m) Now, transaction T₃ issues write operation on data item Z

W_TS(Z)=7, TS(T3)=3 and. R_TS(Z)=7, TS(T3)=3 Since, W_TS(Z)>TS(T3) and also R_TS(Z)>TS(T3) so, this write operation is aborted

n) Now, transaction T₁ issues write operation on data item Z

W_TS(Z)=7, TS(T1)=7 and. R_TS(Z)=7, TS(T3)=7 Since, W_TS(Z)=TS(T3) and also R_TS(Z)=TS(T3) so, this write operation is executed and W_TS(Z)=7

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Schedule 2 -

1) First of all, we will calculate the read and write time stamp of the data items X, Y, Z.

The time stamp of transactions T₁, T₂, T₃ is 1, 3, 7 as the first operation of these transactions is issued on these timestamps.

To find Read time stamp of X, Y, Z

Read timestamp is the largest time stamp when a transaction successfully completes read operation.

R_TS(X)=7 as transaction T₃ successfully completed read operation on it.

R_TS(Y)=7 as transaction T₃ successfully completed read operation on it.

R_TS(Z)=7 as transaction T₃ successfully completed read operation on it.

Write timestamp is the largest time stamp when a transaction successfully completes read operation.

W_TS(X)=1 as transaction T₁ successfully completed write operation on it.

W_TS(Y)=3 as transaction T₂ successfully completed write operation on it.

W_TS(Z)=7 as transaction T₃ successfully completed write operation on it.

2) Now, we will apply basic time stamp ordering protocol which says

if TS_(T) issues W_TS(A) then, it checks 2 conditions

i) If R_TS(A)>TS(T) or W_TS(A)>TS(T) then, abort and rollback T and reject write operation

ii) Otherwise, execute Write operation and update W_TS(A)=TS(T)

if TS_(T) issues R_TS(A) then, it checks 2 conditions

i) If W_TS(A)>TS(T) then, abort and rollback T and reject write operation

ii) Otherwise, execute read operation and update R_TS(A)=Max(TS(T),current R_TS(A)).

a) Now, in this schedule transaction T₁ issues read operation on data item X

W_TS(X)=1, TS(T1)=1 . Since, W_TS(X)= TS(T1) so, this read operation is executed and R_TS(X)=7.

b) Now, transaction T₁ issues read operation on data item Z

W_TS(Z)=7, TS(T1)=1 . Since, W_TS(X)> TS(T1) so, this read operation is aborted.

c) Now, transaction T₂ issues read operation on data item Y

W_TS(Y)=3, TS(T3)=3 . Since, W_TS(X)=TS(T3) so, this read operation is executed.

R_TS(Y)=3

d) Now, transaction T₂ issues write operation on data item Y

R_TS(Y)=7, TS(T2)=3 Since, R_TS(X)>TS(T2) so, this write operation is aborted.

e) Now, transaction T₁ issues write operation on data item X

R_TS(X)=7, TS(T1)=1 Since, R_TS(X)>TS(T1) so, this write operation is aborted.

f) Now, transaction T₃ issues read operation on data item Y

W_TS(Y)=3, TS(T3)=3 . Since, W_TS(X)=TS(T3) so, this read operation is executed.

R_TS(Y)=3

g) T₁ issues write operation on data item Z

W_TS(Z)=7, TS(T1)=1 Since, W_TS(Z)>TS(T1) so, this write operation is aborted.

h) Now, transaction T₂ issues read operation on data item X

W_TS(X)=1, TS(T2)=3 . Since, W_TS(X)<TS(T3) so, this read operation is executed and R_TS(X)=7.

i) Now, transaction T₃ issues read operation on data item X

W_TS(X)=1, TS(T3)=7 Since, W_TS(X)<TS(T3) and so, this read operation is executed and R_TS(X)=7.

j) T₂ issues read operation on data item Z

W_TS(Z)=7, TS(T2)=3.. Since, W_TS(Z)>TS(T3) so, this read operation is aborted.

k) Now, transaction T₂ issues write operation on data item Z

W_TS(Z)=7, TS(T2)=7 and. R_TS(Z)=7, TS(T2)=7 Since, W_TS(X)=TS(T2) and also R_TS(X)=TS(T2) so, this write operation is executed and W_TS(Z)=7

l) Now, transaction T₃ issues read operation on data item Z

W_TS(Z)=7, TS(T3)=7 Since, W_TS(Z)=TS(T3) so, this read operation is executed and R_TS(Z)=7

m) Now, transaction T₃ issues write operation on data item Y

R_TS(Y)=&, TS(T3)=3 Since, R_TS(Y)>TS(T3) so, this write operation is aborted.

n) Now, transaction T₃ issues write operation on data item Z

R_TS(Z)=7, TS(T3)=3 Since, R_TS(Z)>TS(T3) so, this write operation is aborted.

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(b) Testing the serializability of S₁ and S₂ by serialization graph technique to prove that the successful execution of a schedule under BTO will ensure the serializability of the schedule.

Answer - Serialization Graph

There is no cycle in the graph. Hence, it is serializable.

(c) Examine the recoverable characteristic of S₁ and S₂. What schedule (S₁ or S₂) can be executed under the strict timestamp ordering (STO) algorithm and write an equivalent strict schedule for it? We assume that a transaction will be be committed or aborted right after its last operation.

Answer - Recoverable schedules

Schedule 1

Schedule 1 is recoverable with cascading rollback of all the transactions.

Schedule 2

The schedule is recoverable after rollback of all the transactions.

Both the schedules can not be executed under strict time stamp ordering protocol because many operations of the transactions need to be aborted.

Schedule 1

So, this schedule can not be executed under strict two phase locking protocol as transactions t1 and t3 will keep waiting. Even, if the T2 release the lock after commit then, shrinking phase the schedule will start and no new lock can be taken.

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(d) Examine the two-phase locking (2PL) technique on S₁ and S₂ with an assumption of unlock operations being done as late as possible. Are BTO schedules also 2PL schedules?

Answer - Strict 2PL for Schedule 1

Strict 2PL for Schedule 2

No, BTO are not 2PL

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2. Deductive Database

ANCESTOR(X, Y) :- PARENT(X, Y)

ANCESTOR(X, Y) :- PARENT(X, Z), ANCESTOR(Z, Y)

Notice that PARENT(X, Y) means that X, Y are human-beings and Y is the (biological) parent of X; ANCESTOR(X, Y) means that Y is the ancestor of X.

Consider the following fact base: PARENT(john, steve), PARENT(john, olivia), PARENT(olivia, emma), PARENT(olivia, william).

(a) Construct a model theoretic interpretation of the above rules using the given facts.

Answer -

Rules

ANCESTOR(X, Y) :- PARENT(X, Y)

ANCESTOR(X, Y) :- PARENT(X, Z), ANCESTOR(Z, Y)

Known Facts

PARENT(john, steve) is true.

PARENT(john, olivia) is true.

PARENT(olivia, emma) is true.

PARENT(olivia, william) is true.

Parent (X,Y) is false for all other combinations of X,Y

Deduced facts

Ancestor(john, steve) is true.

Ancestor(john, olivia) is true.

Ancestor(olivia, emma) is true.

Ancestor(olivia, william) is true.

Ancestor(john, emma) is true.

Ancestor(john, william) is true.

Ancestor (X,Y) is false for all other combinations of X,Y

(b) State a new rule named as SIBLING(X, Y) and construct a proof theoretic interpretation of this rule to find all siblings.

Answer -

Rule:-

SIBLING(X, Y):-Parent (X,Z),Parent (Y,Z)

if Z is parent of X and also Z is parent Y then, X,Y will be sibling.

Known facts

PARENT(olivia, william) is true.

PARENT(olivia, emma) is true.

PARENT (tony, martin) is true.

PARENT (tony,olivia) is true.

PARENT (john, olivia) is true.

PARENT (john, steve) is true.

PARENT (jenny, tony) is true.

PARENT (david, tony) is true.

PARENT (michael, john) is true.

PARENT (dorothy, john) is true.

PARENT (sophia, jenny) is true.

PARENT (christopher, michael) is true.

Parent (X,Y) is not true for any other combination of X,Y.

Deduced Facts

Sibling (tony, john) is true.

Sibling((jenny, david) is true.

Sibling(Michael,Dorothy) is true.

Sibling(X,Y) is not true for any other combination of X,Y.

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(c) State a new rule named as DESCENDANT(X, Y) and construct a proof theoretic interpretation of this rule to find all descendants of Martin. Note DESCENDANT(X, Y) means Y is a descendant of X.

Answer -

DECENDENT(Z,X) :- PARENT(Z, Y)

DECENDANT(Z,X) :- PARENT(Z,Y), PARENT(Y,X)

DECENDANT(Z,X) states Z is decendant of X

Known facts

PARENT(olivia, william) is true.

PARENT(olivia, emma) is true.

PARENT (tony, martin) is true.

PARENT (tony,olivia) is true.

PARENT (john, olivia) is true.

PARENT (john, steve) is true.

PARENT (jenny, tony) is true.

PARENT (david, tony) is true.

PARENT (michael, john) is true.

PARENT (dorothy, john) is true.

PARENT (sophia, jenny) is true.

PARENT (christopher, michael) is true.

Deduced Facts

DECENADANT(William,Olivia) is true.

DECENADANT(emma,Olivia) is true.

DECENADANT(martin,tony) is true.

DECENADANT(Olivia,tony) is true.

DECENADANT(Olivia,john) is true.

DECENADANT(Steve,john) is true.

DECENADANT(tony,jenny) is true.

DECENADANT(tony,david) is true.

DECENADANT(john,michael) is true.

DECENADANT(john,dorothy) is true.

DECENADANT(jenny,sophia) is true.

DECENADANT(Michael,christopher) is true.

DECENADANT(emma,tony) is true.

DECENADANT(emma,john) is true.

DECENADANT(martin,jenny) is true.

DECENADANT(martin,david) is true.

DECENADANT(john,christopher) is true.

DECENDANT(X,Y) is not true for any other combination X,Y.

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(d) Given the following rules:

FIRST_COUSIN(X, Y) :- PARENT(X, Z), PARENT(Y, T), SIBLING(Z, T)

COUSIN(X, Y) :- FIRST_COUSINS(X, Y)

COUSIN(X, Y) :- PARENT(X, Z), PARENT(Y, T), COUSIN(Z, T)

Note: Two people are first cousins if their parents are siblings. Cousins means any kind of cousins. Cousins can be second cousins who are the children of the two first cousins or third cousins who are the children of two second cousins etc.

1. Prove that FIRST_COUSIN(jenny, michael) is true.

2. Prove that COUSIN(sophia, christopher) is true.

Answer - FIRST_COUSIN(X, Y) :- PARENT(X, Z), PARENT(Y, T), SIBLING(Z, T)

COUSIN(X, Y) :- FIRST_COUSINS(X, Y)

COUSIN(X, Y) :- PARENT(X, Z), PARENT(Y, T), COUSIN(Z, T)

Known facts

PARENT(olivia, william) is true.

PARENT(olivia, emma) is true.

PARENT (tony, martin) is true.

PARENT (tony,olivia) is true.

PARENT (john, olivia) is true.

PARENT (john, steve) is true.

PARENT (jenny, tony) is true.

PARENT (david, tony) is true.

PARENT (michael, john) is true.

PARENT (dorothy, john) is true.

PARENT (sophia, jenny) is true.

PARENT (christopher, michael) is true.

Sibling (tony, john) is true.

Sibling((jenny, david) is true.

Sibling(Michael,Dorothy) is true.

Sibling(X,Y) is not true for any other combination of X,Y.

1) Known Fact

PARENT (jenny, tony) is true.

PARENT (michael, john) is true.

Deduced Fact

From rule 1, FIRST_COUSIN(jenny, michael)is true.

2) Known fact

PARENT (christopher, michael) is true.

PARENT (sophia, jenny) is true.

Deduced Fact

From rule 1, FIRST_COUSIN(christopher, michael)is true.

Hence, From rule2 FIRST_COUSIN(christopher, michael) implies COUSIN(sophia, christopher)

Therefore, COUSIN(sophia, christopher) is true.

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