[ee122] minor corrections to solutions for Homeworks #3 and #4

vern at cs.berkeley.edu vern at cs.berkeley.edu
Sun Dec 16 23:33:45 PST 2007


Appended are corrections/additions to the solutions for a couple of problems
in Homeworks #3 and #4 (both found by students - kudos!, and apologies for
the original errors).

		Vern


[ For Homework #3, the first change is simply "4,x" in the Dijkstra table
  instead being "4,v". ]

Index: hw3_soln.tex
===================================================================
--- hw3_soln.tex	(revision 299)
+++ hw3_soln.tex	(working copy)
@@ -132,13 +132,13 @@
 		Step & N' & D(s),p(s) & D(t),p(t) & D(u),p(u) & D(v),p(v) & D(w),p(w) & D(y),p(y) &D(z),p(z)\\
 		\hline
 		0 & x & $\infty$ & $\infty$ & $\infty$ & 3,x & 6,x & 6,x & $\infty$ \\
-		1 & xv & $\infty$ & 7,v & 6,v & 3,x & 6,x & 4,x & $\infty$ \\
+		1 & xv & $\infty$ & 7,v & 6,v & 3,x & 6,x & 4,v & $\infty$ \\
-		2 & xvy & $\infty$ & 7,v & 6,v & 3,x & 6,x & 4,x & 18,y \\
+		2 & xvy & $\infty$ & 7,v & 6,v & 3,x & 6,x & 4,v & 16,y \\
-		3 & xvyu & 10,u & 7,v & 6,v & 3,x & 6,x & 4,x & 18,y \\
+		3 & xvyu & 10,u & 7,v & 6,v & 3,x & 6,x & 4,v & 16,y \\
-		4 & xvyuw & 10,u & 7,v & 6,v & 3,x & 6,x & 4,x & 18,y \\
+		4 & xvyuw & 10,u & 7,v & 6,v & 3,x & 6,x & 4,v & 16,y \\
-		5 & xvyuwt & 8,t & 7,v & 6,v & 3,x & 6,x & 4,x & 12,t \\
+		5 & xvyuwt & 8,t & 7,v & 6,v & 3,x & 6,x & 4,v & 12,t \\
-		6 & xvyuwt & 8,t & 7,v & 6,v & 3,x & 6,x & 4,x & 12,t \\
+		6 & xvyuwt & 8,t & 7,v & 6,v & 3,x & 6,x & 4,v & 12,t \\
-		7 & xvyuwt & 8,t & 7,v & 6,v & 3,x & 6,x & 4,x & 12,t \\
+		7 & xvyuwt & 8,t & 7,v & 6,v & 3,x & 6,x & 4,v & 12,t \\
 		\hline
 		\end{tabular}
 		}
@@ -149,7 +149,7 @@
 		\small
 		\begin{tabular}{|r|cccccccc|}
 		\hline
-		Step & N' & D(s),p(s) & D(t),p(t) & D(u),p(u) & D(v),p(v) & D(w),p(w) & D(y),p(y) &D(z),p(z)\\
+		Step & N' & D(x),p(x) & D(t),p(t) & D(u),p(u) & D(v),p(v) & D(w),p(w) & D(y),p(y) &D(z),p(z)\\
 		\hline
 		0 & st & $\infty$ & 1,s & 4,s & $\infty$ & $\infty$ & $\infty$ & $\infty$ \\
 		1 & st & $\infty$ & 1,s & 3,t & 5,t & $\infty$ & 8,t & 6,t \\
Index: hw4-soln.tex
===================================================================
--- hw4-soln.tex	(revision 297)
+++ hw4-soln.tex	(working copy)
@@ -158,6 +158,16 @@
 					This gives us \textbf{2 messages per
 					3 slots}.
 
+					However, an alternative interpretation
+					is that B and C can send ACKs to
+					A and D simultaneously, because while
+					these transmissions overlap at B and C,
+					they don't at A and D, and therefore
+					the messages will be successfully
+					received.  In this case, we can
+					get \textbf{2 messages per 2 slot =
+					1 message per slot}.
+
 				\item We have:
 					\begin{description}
 					\item[slot 1] Message from
@@ -167,6 +177,18 @@
 					\end{description}
 
 					This again gives us \textbf{2 messages per 3 slots}.
+
+					Again, an alternative interpretation
+					is that it's possible to synchronize
+					the sending of data from C
+					$\rightarrow$ D with the transmission
+					of \emph{ACKs} from B $\rightarrow$ A,
+					and of data from A $\rightarrow$ B with
+					ACKs from D $\rightarrow$ C.  In this
+					case, on average we can again send
+					\textbf{2 messages per 2 slot =
+					1 message per slot}.
+
 			\end{enumerate}
 		\end{description}
 	\end{enumerate}


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