CS 494/594 -- Distributed Systems --- Fall 2014

Reading Assignments

Homework Assignments

1. (due 9/9) Fill in blanks and do all proofs left to reader in Chapter 3.
2. (due 9/26) (Solutions)
   1. Complete blanks and proofs in Chapters 5 and 6.
   Consider the partial order imposed on students by grades each receives. We say that the grade for student X is "greater or equal" to the grade for student Y (X ≤ Y) if X has recieved a grade no worse than Y in every course. Show that this is a partial order, assuming that all students take exactly the same courses. Is there any total order on all students that extends the partial order? Explain why or why not.
   2. Suppose that a processor used vector time in which each vector element had two components, an "epoch" number and the usual timestamp. A processor that recieved a message with a later "epoch" would update its own epoch to match it, but it would ignore the timestamps on messages it received from an earlier "epoch". A processor could update the epoch in its own timestamp at will. Aside from these rules concerning epochs, the timestamp would be updated and transmitted as usual. What property that such a modifed vector clock guarantee? Can you see an application for such a modified vector timestamp?
   3. Give an algorithm that uses a gossip protocol to compute each of the following:
      1. if an integer value is associated with each node, the maximum of those values.
      2. if an integer value is associated with each node, the sum of those values.
3. (due 11/6)
   1. Complete blanks and proofs in Chapters 7 and 8.
   2. What is the scenario in which the naive solution to the Dining Philosopher's problem leads to deadlock?
   3. How does the hygienic solution maintain the property that there are no cycles in the prioritization of philosophers?
   4. If a consistent cut through a distributed system may not have ever been a true state of the system, why is it considered to be an acceptable state to store and role back to in case of error?
   5. Explain why a snapshot taken at a pre-determined logical time will always be consistent.

Midterm Practice Questions

1. Prove that this program terminates and that at termination N = M*d+r ^ r < M where N and M are initial values.
   
   Program DIV
   var d, r: int
   
   initially d = 0, r = N
   assign
   
   (r ≥ M) → d, r := d+1, r-M
   
   
   
2. How is the value of a vector clock computed? What is the difference between the meaning of an ordinary logical (Lamport) clock and a vector clock?
3. In the diffusion algorithm every node is in one of three states, idle, active or complete. Explain the difference between the active and complete states.
4. Explain Lamport's algorithm for mutual exclusion. A formal proof of correctness is not required, but a clear explanation of the algorithm's functioning is.

Final Practice Questions

1. One way to generate a snapshot of a distributed system is to for every processor to maintain a logical clock, for a logical time T to be predetermined, and for each processor to save its state when its logical clock reaches that time. How do we know that the processor states so saved define a consistent cut, and what further work is necessary to capture a complete snapshot?
2. What must be known about the state of a distributed computation to be able to conclude that it has achieved termination?
3. In the garbage collection algorithm in Chapter 11, it is not sufficient to allow the propagator to simply add and edge pointing to a node that is food. What more must be done and why?
4. State all the requirements of the binary consensus problem.

Semseter Project

Course Grading