Define beneficial semi join. How do you choose best join order in System R algorithm? Explain with example. Descibe hill climbing algorithm to find the initial feasible solution.

by

A beneficial semi join is a type of join optimization technique used in distributed databases, especially when performing joins across sites in a distributed system. The goal is to reduce the amount of data transferred between sites by using a “semi join” approach.

A semi join involves sending only the keys (or attributes) from one table to another rather than sending the entire row of data. This helps in reducing data transmission costs. In a beneficial semi join, the optimization is applied in such a way that the intermediate result set is minimized, thus leading to reduced communication overhead.

Example: Consider two tables in a distributed system:

  • Table A (at Site 1): A (ID, Name)
  • Table B (at Site 2): B (ID, Age)

A regular join would involve sending the entire rows from both tables across sites. In contrast, a semi join would only send the ID values from Table A to Site 2, where it would filter Table B using those ID values and return only the matching rows from Table B back to Site 1.

The beneficial semi join is chosen when the number of keys or attributes to transfer is significantly smaller than the size of the actual data rows, thus saving communication costs.

Choosing the Best Join Order in System R Algorithm

The System R algorithm is used to determine the optimal join order when joining multiple tables in a relational database. The challenge lies in selecting the join order that minimizes the total cost of the query execution, which includes factors like CPU time, I/O costs, and communication overhead.

How to choose the best join order:

  1. Evaluate all possible join orders: For n relations, there are (n-1)! possible join orders. This is a factorial growth, making it impractical to compute every possible order for large numbers of tables.
  2. Use dynamic programming: The System R algorithm uses dynamic programming to evaluate different join orders efficiently by storing intermediate results and minimizing redundant computations.
  3. Cost estimation: For each possible join order, the cost is estimated based on the number of tuples involved and the selectivity of the joins (how many tuples are expected to match).
  4. Iterative process: The algorithm iterates through possible combinations of table pairs to find the most cost-effective way to join the tables.

Example:

Let’s assume we have three tables to join:

  • R1 (A, B)
  • R2 (B, C)
  • R3 (C, D)

The possible join orders are:

  1. (R1 ⋈ R2) ⋈ R3
  2. R1 ⋈ (R2 ⋈ R3)
  3. (R1 ⋈ R3) ⋈ R2

The System R algorithm computes the cost of each possible join order and picks the one with the lowest cost based on available statistics (such as table size, index availability, etc.).

Hill Climbing Algorithm to Find the Initial Feasible Solution

Hill climbing is a search algorithm that starts with an arbitrary solution to a problem and iteratively improves the solution by making small changes. The algorithm is a local search method that always moves to a neighboring state that is better than the current state.

Steps of Hill Climbing Algorithm:

  1. Start with an initial solution: Choose an initial feasible solution, often randomly.
  2. Evaluate the neighbors: Identify neighboring solutions (solutions that are one small step away from the current solution).
  3. Move to the best neighbor: Evaluate the neighbors and move to the one that improves the objective (minimizes or maximizes the value depending on the problem).
  4. Repeat: Repeat this process until no better neighbor can be found, indicating a local optimum.
  5. Stop when no improvement is possible: The algorithm terminates when the current solution is the best it can get in its local neighborhood (i.e., a local maximum or minimum).

Example (Finding the Initial Feasible Solution): Suppose we are trying to solve a traveling salesman problem (TSP) where a salesman needs to visit a set of cities in the shortest possible route. The hill-climbing algorithm works as follows:

  1. Start with a random initial route: Assume the salesman starts at a random city, visiting cities in a random order.
  2. Evaluate neighbors: For each city in the current route, consider swapping it with another city to create a new route.
  3. Move to the best neighbor: Choose the swap that results in the shortest route.
  4. Repeat the process: Keep swapping cities and moving to the shortest route until no further improvements can be made.

Thus, this method guarantees finding a solution, but it may not always find the global optimum because it might get stuck in a local optimum (i.e., a solution that is better than its neighbors but not the best overall).

Leave a Comment