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Mohamed G. Gouda                                        	CS 356
Spring      2007                                        	Homework 3
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1. (5 points)

In a star network p[i:0..n-1], there are two opposite-direction channels between 
process p[0] and each of the processes p[1]..p[n-1]. The processes in this network 
are designed to maintain both local and global topology information. 

a) What is the local and global topology information that need to be maintained 
by each process in this network? 

b) Specify the middle process p[0] and each of the boundary processes p[i:1..n-1] 
in this network. 

c) Write down the condition that allows process p[1] to generate and send a 
data(2) message whose ultimate destination is process p[2]. (Hint: this condition 
involves both the local and global topology information in process p[1].)

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2. (5 points)

The processes in a network p[i:0..n-1] send messages using flooding. Each sent 
message has two fields: data(h,dst) where h is the maximum number of hops that 
this message can still make, and dst is a boolean array of n elements such that 
dst[i] is true iff process p[i] is an ultimate destination of the data message. 
When a process p[i] receives a data(h,dst) from a neighbor p[g], p[i] first checks 
whether it is an ultimate destination of the message, in which case p[i] keeps a 
copy of the message. Then p[i] decrements h by 1 and checks whether the resulting 
h is larger than 0, in which case p[i] forwards a copy of the message to each up 
neighbor other than p[g]. Note that each ultimate destination of a message can end 
up with many copies of the same message. Process p[i] in this protocol is specified 
as follows:

process p[i : 0..n-1]
inp     N   :  set {g | p[g] is a neighbor of p[i]}, 
 	up  :  array[N] of boolean
var     h   :  0..n-1,
	dst :  array[0..n-1] of boolean,
	j   :  0..n
par	g   :  N

begin
	true -> h, dst := n-1, any;
		dst[i] := false;		{p[i] cannot be a destination}
		j := 0;
		do j < n ^ ~dst[j] -> j := j+1
		od;
		if j = n -> skip
		[] j < n -> {send a copy of data(h,dst) to each up neighbor} S0
		fi

[]	rcv data(h,dst) from p[g] -> S1

end

Specify the two statements S0 and S1.

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