3. Several departments around campus have wireless access points, but problems arise if two wireless access points within 200 feet of each other are operating on the same frequency. Suppose the departments with wireless access points are situated as follows: Department: Math Sociology Physics Psychology History English Economics Chemistry Is within 200 feet of departments: Physics, Psychology, Chemistry, Sociology History, English, Economics, Math, Chemistry, Psychology Math, Chemistry Math, Chemistry, Sociology, Economics Sociology, English Economics, Sociology, History English, Sociology, Psychology Math, Psychology, Sociology, Physics 2 a. Draw an undirected graph that represents the table above. b. What is the fewest number of frequencies needed? How could these frequencies be assigned to departments? (Hint: if you need help, Google "graph coloring.")

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
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### Transcript for Educational Website

**Problem Description:**

Several departments around campus have wireless access points, but problems arise if two wireless access points within 200 feet of each other are operating on the same frequency. Suppose the departments with wireless access points are situated as follows:

| Department  | Is within 200 feet of departments:                              |
|-------------|-----------------------------------------------------------------|
| Math        | Physics, Psychology, Chemistry, Sociology                       |
| Sociology   | History, English, Economics, Math, Chemistry, Psychology        |
| Physics     | Math, Chemistry                                                 |
| Psychology  | Math, Chemistry, Sociology, Economics                           |
| History     | Sociology, English                                              |
| English     | Economics, Sociology, History                                   |
| Economics   | English, Sociology, Psychology                                  |
| Chemistry   | Math, Psychology, Sociology, Physics                            |

**Tasks:**

a. **Draw an undirected graph** that represents the table above.

b. **What is the fewest number of frequencies needed?** How could these frequencies be assigned to departments? (*Hint: if you need help, Google "graph coloring."*)

**Graph Explanation:**

- **Vertices (Nodes):** Each department represents a vertex.
  
- **Edges:** An edge exists between two vertices if the corresponding departments are within 200 feet of each other. For example, there is an edge between Math and Physics because they are within 200 feet.

- The graph is undirected because the relationship "is within 200 feet of" is mutual.

**Graph Coloring Concept:**

The goal is to assign the minimum number of different frequencies (colors) such that no two adjacent departments (connected nodes) share the same frequency. This can be approached using graph coloring algorithms.
Transcribed Image Text:### Transcript for Educational Website **Problem Description:** Several departments around campus have wireless access points, but problems arise if two wireless access points within 200 feet of each other are operating on the same frequency. Suppose the departments with wireless access points are situated as follows: | Department | Is within 200 feet of departments: | |-------------|-----------------------------------------------------------------| | Math | Physics, Psychology, Chemistry, Sociology | | Sociology | History, English, Economics, Math, Chemistry, Psychology | | Physics | Math, Chemistry | | Psychology | Math, Chemistry, Sociology, Economics | | History | Sociology, English | | English | Economics, Sociology, History | | Economics | English, Sociology, Psychology | | Chemistry | Math, Psychology, Sociology, Physics | **Tasks:** a. **Draw an undirected graph** that represents the table above. b. **What is the fewest number of frequencies needed?** How could these frequencies be assigned to departments? (*Hint: if you need help, Google "graph coloring."*) **Graph Explanation:** - **Vertices (Nodes):** Each department represents a vertex. - **Edges:** An edge exists between two vertices if the corresponding departments are within 200 feet of each other. For example, there is an edge between Math and Physics because they are within 200 feet. - The graph is undirected because the relationship "is within 200 feet of" is mutual. **Graph Coloring Concept:** The goal is to assign the minimum number of different frequencies (colors) such that no two adjacent departments (connected nodes) share the same frequency. This can be approached using graph coloring algorithms.
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