Randomly Generating Triangulations of a Simple Polygon

Counting Polygon Triangulations is Hard

“…It is sufficiently messy to count the triangulations of active gadgets that we provide here only approximate bounds. However, the exact number of triangulations can be found in polynomial time using the algorithm for counting triangulations of simple polygons [19,32,16]. Figure 6 Encoding the local part of a triangulation by a sequence of bits.…”

“…Necessarily, the polygons of our hardness construction have holes, as it is straightforward to count the triangulations of a simple polygon in polynomial time by dynamic programming [19,32,16]. The polygons resulting from the construction can be drawn with all vertices on a grid of polynomial size.…”

Counting Polygon Triangulations is Hard

“…It is sufficiently messy to count the triangulations of active gadgets that we provide here only approximate bounds. However, the exact number of triangulations can be found in polynomial time using the algorithm for counting triangulations of simple polygons [16,18,31].…”

“…Necessarily, the polygons of our hardness construction have holes, as it is straightforward to count the triangulations of a simple polygon in polynomial time by dynamic programming [16,18,31]. The polygons resulting from the construction can be drawn with all vertices on a grid of polynomial size.…”