06 Feb The third and fourth posts are

MAT2051 Discrete Mathematics

Unit 8 Discussion

DQ1 Networking, Graphs, Adjacency Matrices, and Server Application

Assume you are a network administrator of a large business firm that wishes to construct an intranet. Your firm has a number of computers, servers, and services such as printers, all connected to five hubs (hubs 1, 2, 3, 4, and 5), which must now be connected to each other. Assume each hub is separated by distances shown in the following adjacency matrix:

Adjacency Matrix. See D-Link for full description. [D]

Each hub must be connected to at least one other hub, therefore, you only need to make four connections to allow communication between all computers. You can further minimize the cost of the cables and time by only connecting the closest hubs.

Consider and answer the following questions to evaluate this problem:

What is an intranet?

What is an adjacency matrix, and how do they relate to graphs?

What is the optimal connection of the five hubs that will minimize the length of the cable required to connect them? Note: The length of the cable will be the distance between the hubs as shown in the adjacency matrix.

How did you arrive at this answer? What algorithm should be used to solve this problem?

Hint: This is a graphical minimization problem. Make sure you comment on the following: What are the vertices? What are the weights on the edges? What are we trying to minimize?

Review the Discussion Participation Scoring Guide prior to posting.

Response Guidelines

Read your peers’ posts and respond to two. Compare your response to your peer’s. Explain the similarities and differences between your posts.

DQ2 Practice Problem Set Review

This discussion allows you to work with your peers to complete and understand the assigned problem set for this unit. Remember, two initial posts and two response posts are required. Further posts are optional and recommended:

For the first post, select a problem from this unit’s problem set, write it out fully, solve it fully, and post it.

The second post can be a problem you cannot solve or another fully solved problem from the problem set. If there is a problem in the problem set that you are confused about, write it out fully and show any work that you have started. Note that you are stuck and ask for help. If you are able to solve every problem in the set without difficulty, post at least one other fully solved problem from the set as your second post.

The third and fourth posts are responses. Response guidelines are provided below and in every discussion.

Take advantage of this discussion area to work together as a class on the problem set. Post as many problems as you can and review as many of your peers’ posts as you can. Ask questions. Offer answers. If you are stuck on a problem, post your question. Working as a team will help each person gain a better understanding of the problem set and the concepts covered in this unit. Although the problem set