Algorithmic enumeration of surrounding polygons

Enumerating Empty and Surrounding Polygons

“…Let 𝑆 be a set of 𝑛 points in the Euclidean plane, and let S(𝑆) be the set of surrounding polygons of 𝑆. Yamanaka et al [19] proposed an algorithm that enumerates all the surrounding polygons in S(𝑆) in O (𝑛 2 log 𝑛)-delay and O (𝑛 2 )-space. The enumeration algorithm by Yamanaka et al [19] was designed using the (standard) reverse search. In this section, we modify the algorithm such that it uses the reverse search with child lists.…”

“…We first explain a tree structure over S(𝑆) and the childenumeration algorithm proposed by Yamanaka et al [19] briefly. Next, we explain an enumeration algorithm by using the reverse search with child lists.…”

“…In this subsection, we first describe the enumeration algorithm by Yamanaka et al [19], which uses the reverse search. Then, we modify the algorithm such that it uses the reverse search with child lists.…”

“…Recently, Yamanaka et al [19] proposed surrounding polygons as a new class of simple polygons. For a point set 𝑆, a surrounding polygon of 𝑆 is a simple polygon such that each vertex of the polygon is a point in 𝑆 and every point in 𝑆 is either inside the polygon or a vertex of the polygon.…”