# AATN6385 Project 1 solution

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Original Work
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## Description

The theme of this project is to implement the basic network design model
that is presented in the lecture note entitled “An Application to Network
Design”, and experiment with it.
1. Create software that is capable of doing the following:
• As input, it receives the number of nodes (N), the traffic demand
values (bij Mbit/s) between pairs of nodes, and the unit cost values
for the potential links (aij ).
• As output, the program generates a network topology, with capacities assigned to the links, according to the studied model, using
the shortest path based fast solution method (see at the
end of the referred lecture note). The program also computes the
total cost of the designed network.
Important notes:
• Any programming language and operating system can be used, it
• For the shortest path algorithm you may download and utilize any
existing software module from the Internet. If you use this opportunity, then include in your documentation a precise reference that
tells where the module comes from.
2. Clearly explain how your program works. It is helpful to use flowcharts
for visualizing the explanation.
3. Run your program on examples that are generated as explained below.
• Let the number of nodes be N = 25 in each example.
• For each example, generate the aij , bij values according to the rules
described below. In these rules k is a parameter that will change
in the experiments.
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– For generating the bij values, take your 10-digit student ID,
and repeat it 2.5 times, to obtain a 25-digit number. That is,
the 10-digit sequence is repeated twice, and then the first 5
digits appended again at the end. For example, if the ID is
0123456789, then after repetition it becomes
0123456789012345678901234.
Let d1, d2, . . . , d25 denote the digits in this 25-digit number,
starting from the left. Then the value of bij is computed by
the formula
bij = |di − dj
| Mbit/s.
For example, using the above sample ID, the value of b3,7 will
be b3,7 = |d3 − d7| = |2 − 6| = 4 Mbit/s.
(The reason for using the student ID is that it is unique for everybody, so no two projects can produce completely identical
results.)
– For generating the aij values, do the following. For any given
i, pick k random indices j1, j2, . . . , jk, all different from each
other and from i. Then set
aij1 = aij2 = . . . = aijk = 1,
and set aij = 250, whenever j 6= j1, . . . , jk. Carry out this
independently for every i.
Remark: The effect of this is that for every node i there will
be k low cost links going out of the node, the others will
have large cost. The shortest path algorithm will try to avoid
the high cost links, so it effectively means that we limit the
number of links that go out of the node, thus limiting the
network density.
• Run your program with k = 3, 4, 5 . . . , 13. For each run generate
new random aij parameters independently. The bij parameters
remain the same in all runs, since they only depend on the student
ID.
4. Show graphically in diagrams the following:
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• How does the total cost of the network depends on k?
• How does the density of the obtained network depends on k? Here
the density is defined as the number of directed edges that are
assigned nonzero capacity, divided by the total possible number
of directed edges, which is N(N − 1).
• Show some of the obtained network topologies graphically. Specifically, draw three of them: one with k = 3, one with k = 8, and
one with k = 13.
5. Provide a brief (1-2 paragraph) verbal justification that explains why
the obtained diagrams look the way they do. In other words, try to
convince a reader that what your diagrams show is indeed the “right”
behavior, that is, your program that carries out the network design is
likely correct.
6. Also include a section in the project document that is often referred to
in a software package as ”ReadMe file.” The ReadMe file (or section)
provides instructions on how to run the program. Even though in the
default case we do not plan to actually run the program, we should
be able to do it, if needed. For example, if something does not seem
right, and we want to double check whether the program indeed works
correctly.
Note: If there is anything that is not specified in this project description, it
automatically means that it is left to your choice.
Submission guidelines
Describe everything, including algorithms, program, sources, results and
figures neatly and clearly in a study. Include everything in a single document
that can be read as a report. It should have a professional appearance. For
example, scanned handwriting and hand-drawn figures are not acceptable!
The preferred file type is pdf. Do not submit executable code, but include
the source code as an Appendix in the document. The project report will be
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read as a document and not run as a program (but there are two exceptions,
see them under Evaluation).
Submit the document through eLearning. Do not send it via e-mail!
Notes:
• The work should be fully individual and original. (Except that a shortest path algorithm may be downloaded from the Internet, but it cannot
come from a classmate.) Any form of cheating is a serious violation of
University policies and can lead to serious consequences. Also note
that while there were similar projects in earlier semesters, the exact
same project has never been assigned. The minor differences between
this and earlier similar projects make it easy to detect if a submission
is copied from an earlier one. Furthermore, some of the parameters
depend on the student ID, which is unique for everybody.
• It may be helpful to think about the whole project presentation that
your task is not only to solve a technical problem, but you also have
to “sell” the results. Try to look at your work from the viewpoint of a
potential customer, to whom you want to sell such a software product.
How convincing would your presentation look for a customer?
Evaluation
The evaluation will focus on how well each of the specific tasks have been
carried out, and also on how professional the whole presentation looks.
Note: Even though the submission will not be run, only read as a document, there are two exceptions. You will be asked to demonstrate on a
computer how your program actually runs, if any of the following cases occur:
1. You do not agree with the grade and want to improve it. In this case
the demonstration should show that your work is actually better than