Graph Coloring Concepts and Wi-Fi
For Option #1, you will explore how graph coloring concepts can be applied to the real-world problem of installing Wi-Fi stations in an office. Suppose that an office is installing four Wi-Fi stations throughout the building, and that any stations within 150 feet of each other must transmit on different channels.
Complete the following tasks:
Create your own office configuration and fill in the table with the distances between each pair of Wi-Fi stations in your office. (Note: The maximum distance possible between any two Wi-Fi stations is 200 ft.)
Station #1 Station #2 Station #3 Station #4
Suppose the engineers want to minimize the number of channels. Draw a graph that would be useful to solve this problem. (Hint: Edges should connect two stations when the distance is less than 150 feet.)
Discuss how this problem can be solved using graph coloring concepts.
Solve the problem.
Explain what the chromatic number of the graph you created in part (b) would tell the engineers installing the Wi-Fi stations.