How Database Query Optimizers Work

Problem Description:
Please explain the core function of a database query optimizer, its workflow, and how it selects the optimal execution plan based on a cost model. The explanation should cover key steps in logical optimization (such as predicate pushdown) and physical optimization (such as join algorithm selection).

Solution Process:

1. Core Function of the Query Optimizer

• The Problem: A user-submitted SQL query can typically be executed in multiple ways (e.g., different join orders, index usage strategies), but the execution efficiency can vary significantly.
• Optimizer's Goal: To select the plan with the lowest cost from all possible execution plans while ensuring correct results (cost is usually estimated based on resource consumption like I/O, CPU, memory).
• Analogy: Similar to traveling from Beijing to Shanghai, one can choose high-speed rail, airplane, or driving. The optimizer needs to select the optimal route based on conditions like time and cost.

2. Workflow Overview
The optimizer's work is divided into two core stages:

• Logical Optimization: Rewrites the query based on relational algebra rules to reduce the size of intermediate results.
• Physical Optimization: Selects specific physical operations (e.g., index scan vs. full table scan) for the logical plan and estimates costs.
  It ultimately outputs an executable physical plan.

3. Logical Optimization in Detail
Step 1: Query Parsing and Syntax Tree Generation

• The database first parses the SQL statement to generate an initial logical query tree (e.g., SELECT * FROM A JOIN B ON A.id=B.id WHERE A.age>30).
• Example tree structure:

        [Projection: *]
              |
          [Join: A.id=B.id]
             / \
    [Scan A]    [Scan B]
        |           |
    [Filter: A.age>30]
  

  The initial tree may be inefficient (e.g., scanning the full table before filtering).

Step 2: Applying Logical Optimization Rules

• Predicate Pushdown:
  • Pushes filter conditions (e.g., A.age>30) as close as possible to the data source to reduce the amount of data for subsequent processing.
  • The optimized tree becomes:

          [Projection: *]
                |
            [Join: A.id=B.id]
               / \
    

  [Scan A + Filter A.age>30] [Scan B]

• Column Pruning:
  • Retains only the columns needed in the query (e.g., avoiding scanning unnecessary columns with SELECT *).
• Other rules: Eliminate redundant computations, unnest subqueries, etc.

4. Physical Optimization in Detail
Step 1: Generating Physical Operation Options

• Selects physical implementation algorithms for each operation in the logical plan. For example:
  • Table Scan Methods: Full table scan, index scan (if there's an index on age, data can be located quickly).
  • Join Algorithms:
    • Nested Loop Join: Suitable for small tables driving large tables.
    • Hash Join: Builds a hash table on the join key, suitable for large datasets.
    • Sort-Merge Join: Sorts data first then merges, suitable for already sorted data.

Step 2: Cost Model-Based Estimation

• Cost Estimation Factors:
  • Table size (number of rows, pages), data distribution (histogram statistics), index selectivity (filtering capability).
  • Example: If A.age>30 filters out 90% of the data, an index scan may be far cheaper than a full table scan.
• Join Order Selection:
  • For multi-table joins, the join order affects the size of intermediate results. For example, in A JOIN B JOIN C, if B can filter a large amount of data, joining B and C first might be more optimal.
  • The optimizer enumerates orders via dynamic programming or heuristic algorithms, calculating the total cost for each order.

5. Final Plan Generation and Execution

• The optimizer compares the costs of all candidate plans, selects the optimal one, and generates a physical execution plan (e.g., using an index scan on A, hash join with B).
• The execution engine operates on the data according to the plan and returns the results.

Key Challenges:

• Inaccurate statistics can lead to incorrect cost estimations (e.g., significant deviation between actual data distribution and histogram).
• Enumerating all join orders for multi-table joins can lead to combinatorial explosion, requiring greedy algorithms or search depth limits.

Summary:
The optimizer reduces data volume through logical optimization, selects efficient algorithms through physical optimization, and ultimately relies on the cost model to make decisions. Understanding this process helps in writing optimizer-friendly SQL (e.g., avoiding nested queries, using index-friendly conditions).