By Cattaneo C.

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It is natural to seek better algorithms. Before moving on, however, there are two concerns that need to be addressed. 1. What does it mean for one algorithm to be better than another? 2. Does our algorithm work for all types of point sets in the plane? p 39 40 CHAPTER 2. 6. A point set along with hull points and extreme points. Let’s start with the second question first. At first glance, the incremental algorithm seems to succeed for any point set in the plane. When we look closer, we realize that not all cases have been covered.

8. For a point set S in general position, just as in the gift-wrapping algorithm, choose the rightmost bottom point. Sort the remaining points of S by the angle they form with the horizontal line, from the largest angle to the smallest. From here on, the points are processed in this angularly sorted order. For each point c, a calculation is made to determine whether the two endpoints of the last constructed hull edge ab and c form a left turn or a right turn. 8). This discarding continues as long as the last three points form a right turn.

Cambridge University Press, 2nd edition, 1998. Chapter 1 of this text covers the first three sections of this chapter with a more algorithmic slant. Richard Stanley. Enumerative Combinatorics, Volume I and II. Cambridge University Press, 1997, 1999. This monumental two-volume work covers the art of counting combinatorial objects. The classical text in graduate school. In particular, more than 100 objects are described that are all counted by the Catalan number. Joseph O’Rourke. Art Gallery Theorems and Algorithms.