Query Tree in Relational Algebra

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.

Steps To Make a Query Tree

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.

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.

Let’s understand this using some examples:

Example 1: Consider a relational algebra expression:

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.

Two Relations R and 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).

JOIN R and S where R.P = S.P

Step 3: Now add the root node that on execution gives the output of the query.

Execution Output

Example 2: Suppose we have a query:

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]

The relational algebra expression corresponding to this query:

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.

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.

Step 3: We execute the next operation with the leaf node EMPLOYEE and intermediate node ⋈ _{Mgr_ssn=Ssn}.

Step 4: Now add the root node i.e., π_{Pnumber, Dnum, Lname, Address, Bdate} to get the output of the query on execution.

Features of Query Tree in Relational Algebra

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.
2. Visualization: A query trees provides a visual representation of relational algebra expressions, which helps in debugging queries and understanding query execution plans.
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.

Advantages of Query Tree in Relational Algebra

1. Optimization: Query trees enable query optimization by allowing the database system to explore different execution plans, potentially speeding up query execution time.
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.
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.

Disadvantages of Query Tree in Relational Algebra

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.
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.
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.

FAQs on Query Tree in Relational Algebra

What is the other method used for the internal representation of a query?

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).

What are the three steps necessary before creating the internal representation of a query?

A query must be scanned, parsed, and validated before creating its internal representation (query tree or query graph).

• The scanner identifies the query toke such as SQL keywords, attribute names, and relation names.
• The parser checks the query syntax to determine whether it is formulated according to the query language’s syntax rules (rules of grammar).
• 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.