\assigntitle{5}{21 Nov 97}{VLSI and Pattern Matching}

Please feel free to send me email if there are any ambiguous questions.

\prob{}
Consider the following graph.\\

\centerline{\psfig{file=steiner.ps}}
\begin{description}
\item[A.] Find a minimum cost Rectilinear Steiner Tree (RST) for the following
set of points (the shaded points are the demand points).
\item[B.] Is this an S-RST?  If not show the minimum cost S-RST.
\end{description}

\prob{}
For the following routing problem the three nets $A, B$ and $C$ need
to be connected.
The numbers on the edges represent their lengths, and
assume that the capacity of every edge is 2.\\  

\centerline{\psfig{file=iprog.ps,width=1.8in}}
\begin{description}
\item[A.] Specify an integer (0-1) program for which the solution
gives the minimum total wire length.

\item[B.] Solve the program (you do not need to show your work).
\end{description}

\prob{}
Describe an $O(nm)$ time $O(n + m)$ space algorithm for finding
a minimum cost alignment assuming an affine gap cost model.
Pseudocode with comments would be the best way to describe it.

\prob{} ({\bf Extra Credit.})
Describe an $O(nm \log (m + n))$ time algorithms for finding a minimum
cost alignment assuming the gap cost function $x(k)$ (where $k$ is the length
of the gap) is concave downward
({\em i.e.} the second derivative is always negative).
