# Transactions & schedules - Dependency relations

• MHB
• mathmari
In summary: The dependency relations are:$(T_1, R, B) \to (T_3, W,B)$$(T_1, R, C) \to (T_2, W, C)$$(T_3, R, A) \to (T_4, W, A)$The precedence graphs are:$(T_1, R, B)$ has the highest precedence and $(T_3, R, A)$ has the lowest precedence.The dependency relations are:$(T_1, W, C) \to (T_4, R, C)$
mathmari
Gold Member
MHB
Hey! :giggle:

The below transactions are given :

and the below schedules :

Give the respective dependency relations as well as the precedence graphs. Which schedules are conflict serializable? Which schedules are equivalent?
I reread some notes and looked also for some examples in Google and now I have done the following :

Are the below dependent in $S_1$ ?
$(T_1, R, B) \to (T_3, W,B)$
$(T_1, R, C) \to (T_2, W, C)$
$(T_3, R, A) \to (T_4, W, A)$
$(T_1, W, C) \to (T_4, R, C)$
$(T_4, R, C) \to (T_2, W, C)$
$(T_1, W, B) \to (T_3, W, B)$
$(T_2, R, B) \to (T_3, W, B)$

Then we would get \begin{align*}\text{DEP}(S_1)&=\{(T_1,B,T_3), (T_1, C, T_2), (T_3, A, T_4), (T_1, C, T_4), (T_4, C, T_2), (T_1, B, T_3), (T_2, B, T_3)\}\\ & =\{(T_1,B,T_3), (T_1, C, T_2), (T_3, A, T_4), (T_1, C, T_4), (T_4, C, T_2), (T_2, B, T_3)\}\end{align*}

Is that correct? :unsure:If that is correct then for the other schedules we have :

The dependent ones in $S_2$ are :
$(T_1, R, B) \to (T_3, W,B)$
$(T_1, R, C) \to (T_2, W, C)$
$(T_1, W, C) \to (T_2, W, C)$
$(T_2, R, B) \to (T_1, W, B)$
$(T_1, W, B) \to (T_3, W, B)$
$(T_2, W, C) \to (T_4, R, C)$
$(T_3, R, A) \to (T_4, W, A)$

Then we would get \begin{align*}\text{DEP}(S_2)&=\{(T_1,B,T_3), (T_1, C, T_2), (T_1, C, T_2), (T_2, B, T_1), (T_1, B, T_3), (T_2, C, T_4), (T_3, A, T_4)\}\\ &=\{(T_1,B,T_3), (T_1, C, T_2), (T_2, B, T_1), (T_2, C, T_4), (T_3, A, T_4)\}\end{align*}
The dependent ones in $S_3$ are :
$(T_1, R, B) \to (T_3, W,B)$
$(T_1, R, C) \to (T_2, W, C)$
$(T_1, W, C) \to (T_2, W, C)$
$(T_1, W, B) \to (T_2, R, B)$
$(T_2, R, B) \to (T_3, W, B)$
$(T_2, W, C) \to (T_4, R, C)$
$(T_3, R, A) \to (T_4, W, A)$

Then we would get \begin{align*}\text{DEP}(S_3)&=\{(T_1,B,T_3), (T_1, C, T_2), (T_1, C, T_2), (T_1, B, T_2), (T_2, B, T_3), (T_2, C, T_4), (T_3, A, T_4)\}\\ & =\{(T_1,B,T_3), (T_1, C, T_2), (T_1, B, T_2), (T_2, B, T_3), (T_2, C, T_4), (T_3, A, T_4)\}\end{align*}
The dependent ones in $S_4$ are :
$(T_1, R, B) \to (T_3, W,B)$
$(T_1, R, C) \to (T_2, W, C)$
$(T_1, W, C) \to (T_2, W, C)$
$(T_1, W, B) \to (T_2, R, B)$
$(T_2, R, B) \to (T_3, W, B)$
$(T_2, W, C) \to (T_4, R, C)$
$(T_3, R, A) \to (T_4, W, A)$

Then we would get \begin{align*}\text{DEP}(S_4)&=\{(T_1,B,T_3), (T_1, C, T_2), (T_1, C, T_2), (T_1, B, T_2), (T_2, B, T_3), (T_2, C, T_4), (T_3, A, T_4)\}\\ & =\{(T_1,B,T_3), (T_1, C, T_2), (T_1, B, T_2), (T_2, B, T_3), (T_2, C, T_4), (T_3, A, T_4)\}\end{align*}Is everything correct so far? :unsure:From the precedence graphs we check which are acyclic and these ones are conflict serializable, right?
So $S_3$ and $S_4$ are conflict serializable, right? :unsure:We have that $\text{DEP}(S_3)=\text{DEP}(S_4)$. We have to check if $S_3$and $S_4$ have the same transactions so that we can say that these two schedules are equivalent, right? But exactly does it mean that they have the same transactions? Is it maybe that the schedules $S_3$ and $S_4$ are the same if we reorder some elements? Is that the desired condition that we need? :unsure:

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The notes that I am looking at are these ones from the end of the pdf-page 87.

## 1. What is a transaction in the context of dependency relations?

A transaction is a unit of work that is performed in a database management system. It is a sequence of operations that must be executed as a whole, and either all of its operations are completed successfully or none of them are. In the context of dependency relations, transactions are used to maintain data consistency and ensure that all related transactions are completed successfully before committing changes to the database.

## 2. What are the types of dependency relations in transactions?

There are two types of dependency relations in transactions: data dependency and control dependency. Data dependency occurs when one transaction depends on the data produced by another transaction, while control dependency occurs when the execution of one transaction is dependent on the outcome of another transaction.

## 3. How are dependency relations managed in a database system?

Dependency relations are managed through the use of concurrency control mechanisms, such as locking and timestamp ordering. These mechanisms ensure that transactions are executed in a serializable order and prevent conflicts between concurrent transactions that could lead to data inconsistency.

## 4. What is a schedule in the context of dependency relations?

A schedule is an ordering of the operations of multiple transactions in a database system. It determines the execution order of transactions and can affect the outcome of the data in the database. A schedule is considered serializable if it produces the same result as if the transactions were executed in a serial manner.

## 5. How do dependency relations impact the performance of a database system?

Dependency relations can have a significant impact on the performance of a database system. If not managed properly, conflicts between transactions can lead to delays and inefficiencies in the execution of transactions. However, with proper concurrency control mechanisms in place, dependency relations can be effectively managed to ensure data consistency and optimize performance.

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