CPU architecture: Intel Xeon with 64 bit cores Filesystem: Ext4 with 4KB (4096 byte) blocks The customer records are keyed by a random UUID of 128 bits Customer's Data record definition from the java file: #include cuuid> struct CustomerData { UUID uuid; char[32] name; int ytd_sales; // Customer 128 bit key' 1/ Customer name (char is 2 bytes each)? // Customer year to date sales }; Calculate the size of the internal nodes (M) for our B-tree: Calculate the size of the B-tree leaf nodes (L) for this tree make sure to include the pointer (note CPU architecture!) to keep the list of leaf nodes: UUID UIDUUID UUID UUID UUID CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData Figure #1: Visualization of our B+ Tree of height 2, customer data records, and pointers between the leaf nodes. How tall (on average) will our tree be (in terms of M) with N customer records? If we insert 30,000 CustomerData records, how tall will be tree be? If we insert 2,500,000 customers how tall will the tree be?
CPU architecture: Intel Xeon with 64 bit cores Filesystem: Ext4 with 4KB (4096 byte) blocks The customer records are keyed by a random UUID of 128 bits Customer's Data record definition from the java file: #include cuuid> struct CustomerData { UUID uuid; char[32] name; int ytd_sales; // Customer 128 bit key' 1/ Customer name (char is 2 bytes each)? // Customer year to date sales }; Calculate the size of the internal nodes (M) for our B-tree: Calculate the size of the B-tree leaf nodes (L) for this tree make sure to include the pointer (note CPU architecture!) to keep the list of leaf nodes: UUID UIDUUID UUID UUID UUID CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData Figure #1: Visualization of our B+ Tree of height 2, customer data records, and pointers between the leaf nodes. How tall (on average) will our tree be (in terms of M) with N customer records? If we insert 30,000 CustomerData records, how tall will be tree be? If we insert 2,500,000 customers how tall will the tree be?
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
100%
We are going to design our B+ Tree to be as optimal as possible for
our old hard drives (since the management won’t buy new ones, those
cheapskates!). We want to keep the tree as short as we can and pack each disk block in the filesystem as tightly as possible. We also want to access our
data in sorted order for printing out reports, so each leaf node will have a
pointer to the next one. See figure #1 on next page for a visualization of
our tree.
![### Understanding B+ Trees for Database Storage
#### System Configuration:
- **CPU Architecture**: Intel Xeon with 64-bit cores
- **Filesystem**: Ext4 with 4KB (4096-byte) blocks
- **Customer Records Key**: Random UUID of 128 bits
#### Customer Data Record Structure:
In Java, the customer data record is defined as follows:
```c
#include <uuid>
struct CustomerData {
UUID uuid; // Customer 128-bit key
char[32] name; // Customer name (char is 2 bytes each)
int ytd_sales; // Customer year-to-date sales
};
```
### Calculating Internal Node Size (M) for a B-Tree:
#### B-Tree Leaf Node Calculation:
To determine the size of the B-tree leaf nodes (L) for this structure, consider including the pointer, taking into account the CPU architecture, to maintain the list of leaf nodes.
#### Diagram Explanation:
- **Figure #1**: It provides a visualization of a B+ Tree with a height of 2.
- **Nodes**: Contain UUIDs that serve as keys.
- **Customer Data Records**: Denoted with `CustomerData` blocks.
- **Pointers**: Indicate links between leaf nodes.
### Questions for Understanding:
1. **Tree Height with N Customer Records**:
- How tall, on average, will the tree be in terms of internal nodes (M)?
2. **Height with 30,000 CustomerData Records**:
- If 30,000 customer records are inserted, how tall will the tree be?
3. **Height with 2,500,000 Customers**:
- If 2,500,000 customers are inserted, how tall will the tree be?
This analysis helps in understanding the scalability and efficiency of storing customer records using a B+ Tree structure in a database setting.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85a16b31-7619-4bbb-b006-067a19fea2d2%2F12d9dd2a-c52a-423b-ae94-e47cdb1504a0%2F4qm4wfc_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding B+ Trees for Database Storage
#### System Configuration:
- **CPU Architecture**: Intel Xeon with 64-bit cores
- **Filesystem**: Ext4 with 4KB (4096-byte) blocks
- **Customer Records Key**: Random UUID of 128 bits
#### Customer Data Record Structure:
In Java, the customer data record is defined as follows:
```c
#include <uuid>
struct CustomerData {
UUID uuid; // Customer 128-bit key
char[32] name; // Customer name (char is 2 bytes each)
int ytd_sales; // Customer year-to-date sales
};
```
### Calculating Internal Node Size (M) for a B-Tree:
#### B-Tree Leaf Node Calculation:
To determine the size of the B-tree leaf nodes (L) for this structure, consider including the pointer, taking into account the CPU architecture, to maintain the list of leaf nodes.
#### Diagram Explanation:
- **Figure #1**: It provides a visualization of a B+ Tree with a height of 2.
- **Nodes**: Contain UUIDs that serve as keys.
- **Customer Data Records**: Denoted with `CustomerData` blocks.
- **Pointers**: Indicate links between leaf nodes.
### Questions for Understanding:
1. **Tree Height with N Customer Records**:
- How tall, on average, will the tree be in terms of internal nodes (M)?
2. **Height with 30,000 CustomerData Records**:
- If 30,000 customer records are inserted, how tall will the tree be?
3. **Height with 2,500,000 Customers**:
- If 2,500,000 customers are inserted, how tall will the tree be?
This analysis helps in understanding the scalability and efficiency of storing customer records using a B+ Tree structure in a database setting.
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