INGRES Algorithm (Simplified)
The INGRES Algorithm is used to find the most efficient way to join multiple tables in a database. Its main goal is to minimize the total cost of joining tables by choosing the best order to perform the joins.
How the INGRES Algorithm Works
- Start with the tables: The algorithm starts by looking at each table individually.
- Calculate the cost of joining tables: For every possible pair of tables, the algorithm calculates how expensive it would be to join them.
- Combine tables step by step: The algorithm gradually combines tables by performing the joins. At each step, it keeps track of the lowest-cost join combination.
- Choose the best order: After considering all possible ways to join the tables, the algorithm picks the join order that results in the least cost.
Example of the INGRES Algorithm
Let’s say you have three tables: A, B, and C. You want to join them together. The cost of joining them depends on their sizes:
- Table A has 1000 rows.
- Table B has 500 rows.
- Table C has 200 rows.
Let’s assume the cost of joining pairs of tables is as follows:
- Cost of A ⨝ B = 1000 * 500 = 500,000
- Cost of A ⨝ C = 1000 * 200 = 200,000
- Cost of B ⨝ C = 500 * 200 = 100,000
Now, we need to figure out the best order to join these three tables.
- Option 1: First, join A and B, then join the result with C.
- Cost of joining A and B: 500,000
- Cost of joining the result with C: 500,000 * 200 = 100,000,000
- Option 2: First, join A and C, then join the result with B.
- Cost of joining A and C: 200,000
- Cost of joining the result with B: 200,000 * 500 = 100,000,000
- Option 3: First, join B and C, then join the result with A.
- Cost of joining B and C: 100,000
- Cost of joining the result with A: 100,000 * 1000 = 100,000,000
In this example, all three options have the same cost of 100,000,000. But the INGRES algorithm would normally select the option with the lowest cost, especially when the costs differ.
System R Algorithm (Simplified)
The System R Algorithm is another method for choosing the best join order, used in databases to optimize query performance. This algorithm works by evaluating all possible join orders and picking the one with the lowest cost.
How the System R Algorithm Helps
- Evaluate pairs of tables: The algorithm starts by looking at pairs of tables and calculating the cost of joining them.
- Combine tables: The algorithm then combines these tables into a new intermediate result and calculates the cost of joining this intermediate result with other tables.
- Keep track of costs: It continues this process until all the tables are joined.
- Choose the best order: The algorithm selects the join order with the least total cost.
Example of the System R Algorithm
Let’s use the same three tables: A, B, and C.
- Cost of A ⨝ B = 1000 * 500 = 500,000
- Cost of A ⨝ C = 1000 * 200 = 200,000
- Cost of B ⨝ C = 500 * 200 = 100,000
We need to check the costs of all possible join orders:
- Option 1: First, join A and B, then join with C.
- Cost: 500,000 + (500,000 * 200) = 100,000,000
- Option 2: First, join A and C, then join with B.
- Cost: 200,000 + (200,000 * 500) = 100,000,000
- Option 3: First, join B and C, then join with A.
- Cost: 100,000 + (100,000 * 1000) = 100,000,000
Like the INGRES algorithm, the System R algorithm would choose the join order with the lowest cost, though in this case, all three options have the same cost.
Figures (Illustrative Diagram)
- Possible Join Orders for tables A, B, and C:
Join Order 1: (A ⨝ B) ⨝ C Join Order 2: (A ⨝ C) ⨝ B Join Order 3: (B ⨝ C) ⨝ A - Cost Calculation for Each Join Order:
Join Order 1: Cost(A ⨝ B) = 500,000 -> Cost((A ⨝ B) ⨝ C) = 500,000 * 200 = 100,000,000 Join Order 2: Cost(A ⨝ C) = 200,000 -> Cost((A ⨝ C) ⨝ B) = 200,000 * 500 = 100,000,000 Join Order 3: Cost(B ⨝ C) = 100,000 -> Cost((B ⨝ C) ⨝ A) = 100,000 * 1000 = 100,000,000
Thus, both the INGRES algorithm and the System R algorithm are used to optimize queries by finding the best way to join multiple tables. They calculate the cost of different join orders and select the one that minimizes the total cost. While these algorithms may give the same results in some cases, they help to make sure that queries run as efficiently as possible, especially in complex database systems with multiple joins.