CS255 Spring 2015Practice Midterm

To study for the midterm I would suggest you: (1) Know how to do (by heart) all the practice problems. (2) Go over your notes at least three times. Second and third time try to see how much you can remember from the first time. (3) Go over the homework problems. (4) Try to create your own problems similar to the ones I have given and solve them. (5) Skim the relevant sections from the book. (6) If you want to study in groups, at this point you are ready to quiz each other. The practice midterm is below. Here are some facts about the actual midterm: (a) It is closed book, closed notes. Nothing will be permitted on your desk except your pen (pencil) and test. (b) You should bring photo ID. (c) There will be more than one version of the test. Each version will be of comparable difficulty. (d) One problem (less typos) on the actual test will be from the practice test.

1. Give the definition of a probability distribution. Define and give an example of pairwise independence.
2. Show that if the candidates are presented in random order, then algorithm Hire-Assistant has a hiring cost of `O(c_h cdot ln n)`.
3. Suppose we get a uniformly randomly chosen coupon on a daily basis from a set of `n` distinct coupons. Calculate showing your work how many days on average until one would expect to have acquired `n/2` distinct coupons.
4. What is a concurrency platform? What is nested parallelism? What is static threading?
5. Prove the span law. Prove the work law.
6. Prove the running time `T_P` of any multithreaded computation scheduled by a greedy scheduler on an ideal parallel computer with `P` processors is within a factor of 2 of optimal.
7. What is a determinancy race condition? Give an example.
8. Give the randomized PRAM algorithm for maximal independent set described in class. Analyze its run time.
9. Explain what could go wrong with our algorithm for Byzantine Agreement if more that 1/8 of the processors are faulty.
10. Briefly give the algorithm to simulate PRAMs using map reduce jobs from class.