CS 6/73201 "Advanced Operating Systems"

	       HOMEWORK #2

	Due in class on 3/23/2010


1. Auerbach's algorithm is a modification of the classical depth-first
   traversal algorithm. The major change is that two new types
   of messages are introduced: <vis> and <ack> and the update
   rules for "used" array are modified. As a consequence of that
   it becomes necessary to explicitly require that only the
   initiator decides (notice that in Tarry's and Classical traversal
   algorithm it is done implicitly -- the only process that
   can possibly decide is the initiator). Explain why it is necessary
   and give an example where the Auerbach's algorithm _without_
   this particular modification fails.


2. In Auerbach's algorithm. When a process P receives <tok> message it
   first sends <vis> message to every neighbor, waits for <ack> from
   every neighbor and then proceeds to forward <tok>.

   Would the algorithm be correct if a process does not wait for
   <ack>s to come back but forwards <tok> immediately after <vis>
   messages are sent?  If yes, explain why; if no, explain why and
   provide a counter-example.


3. If each process uses a different value "d" (increment) in Lamport's
   logical clocks, do the clocks still preserve the causality relationship?

   That is, for two events A and B:

        if A -> B  then C(A) < C(B)

   Explain your answer.

4. Consider the system of three processes (A,B,C) and the following
   computation:

        [B sends message M1 to C], [B sends M2 to A], [A receives M2],
        [A sends M3 to B], [A sends M4 to C], [C receives M4],
        [C receives M1], [C sends M5 to B], [B receives M5], [B receives M3]

   Apply SES causal message delivery algorithm. Draw a timing diagram
   of message receipts and deliveries according to SES.


5. 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.


6. Modify Chandy-Lamport's global state recording algorithm
   such that it always records transitless global state. Explain
   how your modification operates.


7. 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. 

   
8. 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?


9. 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


10. 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.


11. 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.

12. 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