A Query Tree is a data structure used for the internal representation of a query in RDBMS. It is also known as the Query Evaluation/Execution Tree. The leaf nodes of the query tree represent the relations, and the internal nodes are the relational algebra operators like SELECT (σ), JOIN (⋈), etc. The root node gives the output of the query on execution.
查詢樹是一種用於RDBMS中查詢的內部表示的資料結構。它也稱為查詢評估/執行樹。查詢樹的葉節點表示關係，內部節點是關係代數運算符，如 SELECT ( σ )、JOIN ( ⋈ ) 等。

Steps To Make a Query Tree
製作查詢樹的步驟

Step 1: Execute the leaf nodes with their corresponding internal nodes having the relational algebra operator with the specified conditions to get the resulting tuples that we use for the execution of the next operation.
步驟1：在指定的條件下執行葉節點及其對應的具有關係代數運算子的內部節點，以獲得我們用於執行下一個操作的結果元組。

Step 2: This process continues until we reach the root node, where we PROJECT (π) the required tuples as the output based on the given conditions.
步驟2：這個過程一直持續到我們到達根節點，在那裡我們根據給定的條件投影（ π ）所需的元組作為輸出。

Let’s understand this using some examples:
讓我們用一些例子來理解這一點：

Example 1: Consider a relational algebra expression:
範例 1：考慮一個關係代數表達式：

πp (R ⋈ R.P = S.P S)

Step 1: Write the relations you want to execute as the tree’s Leaf nodes. Here R and S are the relations.
第 1 步：將要執行的關係寫入樹的葉節點。這裡R和S是關係。

Two Relations R and S
兩個關係 R 和 S

Step 2: Add the condition (here R.P = S.P) with the relational algebra operator as an internal node (or parent node of these two leaf nodes).
步驟2：新增以關係代數運算子作為內部節點（或這兩個葉子節點的父節點）的條件（此處RP = SP）。

JOIN R and S where R.P = S.P
連接 R 和 S，其中 RP = SP

Step 3: Now add the root node that on execution gives the output of the query.
步驟 3：現在新增根節點，該根節點在執行時會提供查詢的輸出。

Execution Output  執行輸出

Example 2: Suppose we have a query:
範例 2：假設我們有一個查詢：

For every project located at ‘Stanford’, list the project number (Pnumber), the controlling department number (Dnum), and the department manager’s last name (Lname), address (Address), and birth date (Bdate). [1]
對於位於「史丹佛」的每個項目，列出項目編號 (Pnumber)、控制部門編號 (Dnum) 以及部門經理的姓氏 (Lname)、地址 (Address) 和出生日期 (Bdate)。 [1]

The relational algebra expression corresponding to this query:
此查詢對應的關係代數表達式：

πPnumber, Dnum, Lname, Address, Bdate(((σPlocation = ‘Stanford’(PROJECT)) ⋈ 
Dnum=Dnumber(DEPARTMENT)) ⋈ Mgr_ssn=Ssn(EMPLOYEE))

Step 1: We will begin with executing the first leaf node PROJECT, and the corresponding internal node σ_{Plocation = ‘Stanford’} as we need these resulting tuples to execute the next operation.
步驟 1：我們將從執行第一個葉節點PROJECT和對應的內部節點σ _{Plocation = 'Stanford'}開始，因為我們需要這些結果元組來執行下一個操作。

Step 2: Similarly, we will execute the leaf node DEPARTMENT and the intermediate/internal node ⋈ _Dnum=Dnumber so that we can move to the next operation.
步驟2：同樣，我們將執行葉子節點DEPARTMENT和中間/內部節點⋈Dnum _=Dnumber，以便我們可以進行下一個操作。

Step 3: We execute the next operation with the leaf node EMPLOYEE and intermediate node ⋈ _{Mgr_ssn=Ssn}.
步驟3：我們用葉子節點EMPLOYEE和中間節點⋈Mgr_ssn _=Ssn執行下一個操作。

Step 4: Now add the root node i.e., π_{Pnumber, Dnum, Lname, Address, Bdate} to get the output of the query on execution.
步驟 4：現在新增根節點，即π _{Pnumber、Dnum、Lname、Address、Bdate}以取得執行時查詢的輸出。

Features of Query Tree in Relational Algebra
關係代數中查詢樹的特點

1. Hierarchical Structure: Query trees organize relational algebra operations into a hierarchical structure, making it easier to understand the sequence of operations in a query.
   分層結構：查詢樹將關係代數運算組織成分層結構，因此更容易理解查詢中的操作順序。
2. Visualization: A query trees provides a visual representation of relational algebra expressions, which helps in debugging queries and understanding query execution plans.
   視覺化：查詢樹提供關係代數表達式的視覺化表示，這有助於偵錯查詢和理解查詢執行計劃。
3. Optimization Potential: Query trees allow database systems to apply optimization techniques such as reordering operations or using alternative access paths to improve query performance.
   優化潛力：查詢樹允許資料庫系統應用最佳化技術，例如重新排序操作或使用替代存取路徑來提高查詢效能。

Advantages of Query Tree in Relational Algebra
關係代數中查詢樹的優點

1. Optimization: Query trees enable query optimization by allowing the database system to explore different execution plans, potentially speeding up query execution time.
   最佳化：查詢樹透過允許資料庫系統探索不同的執行計劃來實現查詢最佳化，從而可能加快查詢執行時間。
2. Modularity: Query trees break complex queries into smaller and more manageable components. Which can facilitate the optimization process and make it easier to reason about query execution.
   模組化：查詢樹將複雜的查詢分解為更小、更易於管理的元件。這可以促進優化過程並更容易推理查詢執行。
3. Flexible Optimization Strategies: Database systems can use query trees to implement various optimization strategies, such as join reordering, predicate pushdown, and index selection, to improve query performance.
   靈活的最佳化策略：資料庫系統可以使用查詢樹來實現各種最佳化策略，例如連接重排序、謂詞下推、索引選擇等，以提高查詢效能。

Disadvantages of Query Tree in Relational Algebra
關係代數中查詢樹的缺點

1. Complexity: Query trees can be complex, especially for large and complex queries. Managing and optimizing these trees can require significant computational resources and sophisticated optimization algorithms.
   複雜性：查詢樹可能很複雜，尤其是對於大型且複雜的查詢。管理和最佳化這些樹可能需要大量的運算資源和複雜的最佳化演算法。
2. Overhead: Building and traversing the query tree imposes overhead on query processing. Although this overhead is usually negligible for small queries, it can be significant for larger queries with many functions.
   開銷：建置和遍歷查詢樹會為查詢處理帶來開銷。儘管這種開銷對於小型查詢來說通常可以忽略不計，但對於具有許多函數的大型查詢來說可能會很重要。
3. Limited Optimizations: Despite their ability to optimize, query trees may not always yield significant performance improvements. In some cases, the overhead associated with optimization may exceed the performance gain achieved through query optimization.
   有限的優化：儘管查詢樹具有優化能力，但它們可能並不總是能帶來顯著的效能改進。在某些情況下，與最佳化相關的開銷可能超過透過查詢最佳化實現的效能增益。

FAQs on Query Tree in Relational Algebra
關係代數中查詢樹的常見問題解答

What is the other method used for the internal representation of a query?
用於查詢的內部表示的其他方法是什麼？

The other possible way to represent a query is by using a graph data structure called a query graph. A query graph is generally a Directed Acyclic Graph (DAG).
表示查詢的另一種可能的方式是使用稱為查詢圖的圖形資料結構。查詢圖通常是有向無環圖（DAG）。

What are the three steps necessary before creating the internal representation of a query?
在建立查詢的內部表示之前需要執行哪三個步驟？

A query must be scanned, parsed, and validated before creating its internal representation (query tree or query graph).
在建立查詢的內部表示（查詢樹或查詢圖）之前，必須先對查詢進行掃描、解析和驗證。

• The scanner identifies the query toke such as SQL keywords, attribute names, and relation names.
  掃描器識別查詢令牌，例如 SQL 關鍵字、屬性名稱和關係名稱。
• The parser checks the query syntax to determine whether it is formulated according to the query language’s syntax rules (rules of grammar).
  解析器檢查查詢語法以確定它是否是根據查詢語言的語法規則（語法規則）制定的。
• The query must also be validated by checking that all attribute and relation names are valid and semantically meaningful names in the schema of the particular database being queried.
  還必須透過檢查所有屬性和關係名稱在所查詢的特定資料庫的模式中是否有效且具有語義意義的名稱來驗證查詢。

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Article Tags :

• DBMS
• DBMS-Relational Algebra