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Mohamed G. Gouda						Midterm 3
CS 356: Computer Networks					Spring 2007O
Open Book							75 Minutes
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1. (10 points)
In a network p[i:0..4], the following six process pairs are neighbors: 
{p[0],p[1]}, {p[0],p[2]}, {p[1],p[2]}, {p[1],p[3]}, {p[2],p[4]}, {p[3],p[4]}

The processes in the network employ the protocool in Section 11.3 to maintain 
global topology information. At some instant, process p[3] has the following 
net array, where F stands for False and T stands for True. 

     0	 1   2   3   4
   +---+---+---+---+---+
 0 | F | T | T | F | F | 
   +---+---+---+---+---+
 1 | T | F | T | F | F | 
   +---+---+---+---+---+
 2 | T | T | F | F | F | 
   +---+---+---+---+---+
 3 | F | F | F | F | T | 
   +---+---+---+---+---+
 4 | F | F | F | T | F | 
   +---+---+---+---+---+

Based on this net array, process p[3] can determine all the process pairs that 
it is sure that they are neighbors and that the two channels between them are up. 
Please list all the process pairs that p[3] is sure that they are neighbors and 
the two channels between them are up. Explain your answer. 

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2. (10 points)
Consider a "mesh" network p[i:0..m-1, j:0..n-1] where each process p[i,j] has the 
following neighbors:
	p[(i-1), j], provided i>0
	p[(i+1), j], proivded i<m-1
	p[i, (j-1)], provided j>0
	p[i, (j+1)], provided j<n-1

The processes in this network generate data messages and route them to their 
ultimate destinations. A specification of process p[i,j] in this network is as 
follows:

process p[i:0..m-1, j:0..n-1]
inp     N : set { (i`,j`) | 
			    [i`=i ^ (j < n-1 => j`=j+1) ^
				    (j > 0   => j`=j-1) ]

			 V  [j`=j ^ (i < m-1 => i`=i+1) ^
				    (i > 0   => i`=i-1) ]
		}	
	up : array [N] of boolean 	{all true}
var     x  : 0..m-1,  y : 0..n-1	{ultimate destination of data msg}
par 	g  : N				{any neighbor}
begin
	true -> x,y := any, any; RTMSG

[]	rcv data(x,y) from p[g] -> RTMSG
end

Specify the statement RTMSG ensuring that the data messages are distributed along 
thier shortest routes. Does your specified RTMSG achieve load-balancing? Explain 
your answer.
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