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CS 763 Fall 2020 \hfill due Thursday September 24\\
{A.~Lubiw \hfill \quad}
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\large\bf ASSIGNMENT 2
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ACKNOWLEDGE YOUR SOURCES.

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\item{[10 marks]}  
In class we covered Graham's algorithm to find the convex hull of points in 2D.  The first step is to sort the points radially around a central point so we have a simple polygon $p_1, p_2, \ldots, p_n$. The second step is to process this polygon in linear time, by repeatedly removing the second last point in the path if it is reflex.  (Details can be found in the class slides, or on the internet.)

Does the second step work to find the convex hull of any simple polygon in linear time?  
Prove your answer.  


 
\item{[10 marks]} 
Give a polynomial time algorithm that takes a simple polygon $P$ as input and finds, if it exists, a triangulation of $P$ whose dual is a path.  Justify correctness, and analyze the runtime of your algorithm.

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