Capella MAT2051 Unit 8 Discussion (dq1+dq2) Latest 2019 October

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 sets are not graded they will help you prepare for the quizzes in
this course.

Response
Guidelines

The third
and fourth posts, the response posts, are your chance to help your peers.
Explore the posts made by your peers and find people who are stuck. Help at
least two peers through the problems they are stuck on. If you are unable to
locate a peer who is stuck, you may instead choose a peer post, write out your
solution to the same problem, and compare solutions and methods. The goal of this
area is for the entire class to work together as a group on the entire problem
set. You are also expected to complete and understand the problem set on your
own in preparation for the quizzes and final exam.