Test 1 for the course

CS 4365/CS 5354, Spring 2015

Name: _____________________________________________________

1. Briefly explain the differences and similarities between private cloud, public cloud, and community cloud.

2. Solve the following constraint optimization problem: minimize
the expression x^{2} + 2y^{2} under the constraint
2x + y = 1. Give two examples when optimization is important for
cloud computing.

3. Use Least Squares to find, step-by-step, the parameters m and b
for which y_{i} ~ m * x_{i} + b, when
x_{1} = −1, x_{2} = 0, x_{3} = 1,
y_{1} = −0.9, y_{2} = 0.0, and y_{3}
= 1.1.

4. Explain, step-by-step, how, given the values x_{i} and
y_{i}, we can find the parameters of the corresponding
power law y ~ A * x^{α}. Explain why this problem is
important for cloud computing.

5-7. In the RSA algorithm, let us start with the prime numbers p = 3 and q = 5, and let us take e = 5. Show, step-by-step, how the RSA algorithm will generate the secret code d, and how it will encode the message m = 3. Then decode and check that you get the original message back. Use the actual RSA algorithms on all steps, do not just guess for d and raise to the power to encode. Why is security especially important for cloud computing?

8. Show how, given seven numbers a_{1}, a_{2},
..., a_{7}, we can compute the partial sums s_{1}
= a_{1}, s_{2} = a_{1} + a_{2},
s_{3} = a_{1} + a_{2} + a_{3},
..., s_{7} = a_{1} + a_{2} + ... +
a_{7} in parallel. Why cloud computing strongly encourages
parallelization?

9. Explain how to use MapReduce to find the largest of n values.

10. Briefly describe what you have done for your project.