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4 Answers

9 votes
9 votes

Structuring the schedule like this :
 

T1 T2 T3 T4
$\color{Red}{W(A)}$      
$\color{Blue}{W(B)}$      
  $\color{Magenta}{R(A)}$    
  $\color{Blue}{W(B)}$    
    $\color{Magenta}{R(A)}$  
    $\color{Blue}{W(B)}$  
      W(C)
  • The Write of $T_1$ on $A$ is conflicting with Read of $T_2$ and $T_3$
  • The Write of on $B$ of $T_1$ $T_2$ $T_3 $is conflicting with each other.
  • Write of $T_3$ is free.

 Whenever there is a conflict operation , the order of original schedule should be maintained.

 W(C) can be perform any time and R(A) of both transaction can be performed anytime after Write of T1.


$\therefore \ 2 $ positions for $R_2(A)$ $2$ for $R_3(A)$ and order can be changed so $2!$ for order change.

Total  $2 \times 2 \times 2=8$

For these $8$ schedules W(C) can be done at any time because its not a conflicting operation .


Total places in schedule which is feasible for $T_4(C)=7$

So total schedules = $8 \times 7=\color{Red}{56}$

1 votes
1 votes
R4(c) can be placed to any seven position as it is independent

Remaining 3 transition can be placed in 8 way (2*2*2)

So total no of conflict is 8*7=56
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0 votes

Looking at the precedence Graph, we get

                                   

So from here, we can see that any transaction of T1 should happen before T2 & T3 and any transaction of T2 should happen after T1 and before T3 and any transaction of T3 should happen after T1 & T2.

Let us ignore W4(C) for now since that can occur anywhere among 7 possible places.

So for | W1(A),W1(B)  R2(A),W2(B)  |  R3(A),W3(B) | none of the separated Read/Write can occur in/before/after the next/previous separated section since that will violate our above condition.

So possible permutations are limited only among the Reads/Writes of One single Underlined section.

So Possible number of permutations are 2*2*2=8

Consider W4(C) and its 7 possible places, we get 7*8=56 possible permutations.

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0 votes

​​​​​​following is the pictorial explanation... here at the time of finding position for r2(a) and r3(a) keep in mind that conflict precedence should not alter..

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