A. Please define a B-tree of Order 2 and draw a B-tree example with sample records. Explain why B-trees are often used in relational DBMS. (30 points) B. Please present the data structure and algorithm used in the ID3 inductive learning method. (30 points) C. Please present a business problem that is suited for using ID3. Please explain the characteristics of your problem and the steps (for your business problem) involved to perform your knowledge discovery task. (40 points) APA 2 references

A. B-trees are a type of self-balancing search tree data structure that is commonly used in relational database management systems (DBMS). A B-tree of Order 2 is a specific type of B-tree where each node can have at most 2 children. The B-tree is an m-ary tree, where m can vary depending on the implementation, and each node can have at most m-1 keys.

To understand the structure of a B-tree of Order 2, let’s consider an example. Assume we have a B-tree that stores records with integer keys and values. The B-tree can be visualized as follows:

9

/

3 13

/ /

1 5 11 15

In this example, each node can have at most 2 children. The root node contains the key 9. The left child of the root contains the keys 3 and 5, and the right child of the root contains the keys 11 and 13. The leaf nodes at the bottom of the tree contain the keys 1 and 15.

B-trees are often used in relational DBMS because they provide efficient searching, insertion, and deletion operations. Here are a few reasons why B-trees are preferred in DBMS:

1. Balancing: B-trees are self-balancing data structures, meaning that the height of the tree is minimized, and the tree remains well-balanced even after frequent insertions and deletions. This ensures that the performance of search operations remains consistent regardless of the size of the dataset.

2. Support for range queries: B-trees are efficient in handling range queries as they allow for easily traversing the tree to retrieve all records within a specified range. This is crucial for database systems that need to retrieve data based on a range of values, such as retrieving all records with a certain timestamp.

3. Efficient disk access: B-trees are optimized for disk access patterns. Their structure allows for minimizing disk I/O operations by maximizing the number of keys and values stored in a single disk page. This reduces the number of disk reads and writes required, thus improving database performance.

B. The ID3 algorithm is a popular inductive learning method used for building decision trees from a given dataset. It is commonly used in machine learning and data mining.

The ID3 algorithm follows a top-down, greedy approach to construct a decision tree. It uses an information gain criterion to measure the importance of different attributes in the dataset. The algorithm operates as follows:

1. Start with the entire dataset and calculate the entropy of the target variable (e.g., the class variable). Entropy measures the impurity or randomness in a set of examples.

2. For each attribute in the dataset, calculate the information gain, which is a measure of how much the attribute contributes to reducing the impurity in the dataset. The attribute with the highest information gain is selected as the root of the decision tree.

3. Partition the dataset based on the chosen attribute and create a branch for each possible attribute value. Recursively apply steps 1-2 to each partitioned subset.

4. Repeat steps 1-3 until one of the following conditions is met: all attributes have been used, all instances in a subset have the same class label, or there are no more instances left in the subset.

5. Assign the class label based on the majority class in the leaf node.

The ID3 algorithm is easy to implement and provides interpretable decision trees. However, it has limitations, such as the inability to handle continuous attributes directly and the tendency to overfit the training data.

C. A business problem suited for using ID3 could be customer churn prediction for a subscription-based service. In this problem, the aim is to identify factors that contribute to customer churn and predict which customers are likely to leave the service.