CS 6/73201 "Advanced Operating Systems"

	       HOMEWORK #2

	Due in class on 11/01/2006


The numbers in parenthesis refer to "Introduction to Distributed
Algorithms" (IDA)

1. Notice that the size of the matrix clock is quadratic with respect
   to the system size. Propose a technique similar to that of
   Singhal-Kshemkalyani to decrease the information transmitted and
   stored if the clocks do not change frequently.


2. Apply Shavit-Francez termination algorithm to the tree based

   A   B
    \ /
     C
     |
     D
    / \
   E   F

   wave algorithm.  Explain how it can run, show a possible
   computation of the tree algorithm and Shavit-Francez termination
   detection on top of it. 
   
3. (AOS 6.2) Show that in Lamport's mutual exclusion algorithm, if
   process Pi is in the CS, then Pi's request may not be at the top of
   the request queue of another process Pj. Is it still true when
   there are no messages in transit?

4. Show that in the Ricart-Agrawala's algorithm, the critical section
   is accessed according to the increasing order of timestamps
   (discuss why it is impossible for the CS to be granted out of
   timestamp order).

   Give an example (draw diagrams) where the CS is granted out of
   timestamp order in Maekawa's algorithm

5. Discuss why FAILED message is needed in Maekawa's algorithm.  Give
   an example (draw diagrams) where the algorithm performs incorrectly
   if FAILED message is not used.

6. Suzuki-Kasami DMX algorithm requires that the token carries an
   array of the number satisfied requests (LN) for each process.
   Since the unsatisfied requests are stored in a queue (Q) held by
   the token would it be possible to determine which requests are
   satisfied and dispense with the array LN altogether?  Explain your
   answer.

7. Consider the network structure below. The processes are executing
   Raymond's token circulation DMX algorithm. Process A initially holds
   the token and processes C,D and E are in CS contention. Is it
   possible that requesting processes enter critical section
   in the following order D,C,E? Explain your answer. Draw a sequence
   of diagrams outlining the possible computation.

             oA
            / \
           oB  oC
          / \
         oD  oE

8. The philosophers are social and only eat in the company of their
   neighbors. Arbitrary topology. Philosophers alternate between
   thinking, and eating (there is no getting hungry state - as soon as
   the philosopher becomes hungry, the philosopher starts to
   eat). However, as the philosophers eat, they look at each other
   (the application controls when the process gets into critical
   section, the solution controls how long the process can remain in
   the critical section). One assumption is that if a philosopher is
   eating, eventually, its every neighbor will be eating as well.

   Propose a solution that ensures the following two properties:

  a. If a philosopher is eating, it can stop eating only if all of its
     neighbors are eating.

  b. An eating philosopher eventually stops. 

  Note, that the computations of a solution are always infinite. Think
  as to why.