Efficient Enumeration of At Most $k$-Out Polygons
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918141675700224 |
|---|---|
| author | Akram, Waseem Yamanaka, Katsuhisa |
| author_facet | Akram, Waseem Yamanaka, Katsuhisa |
| contents | Let $S$ be a set of $n$ points in the Euclidean plane and general position i.e., no three points are collinear. An \emph{at most $k$-out polygon of $S$} is a simple polygon such that each vertex is a point in $S$ and there are at most $k$ points outside the polygon. In this paper, we consider the problem of enumerating all the at most $k$-out polygon of $S$. We propose a new enumeration algorithm for the at most $k$-out polygons of a point set. Our algorithm enumerates all the at most $k$-out polygons in $\mathcal{O}(n^2 \log{n})$ delay, while the running time of an existing algorithm is $\mathcal{O}(n^3 \log{n})$ delay. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12696 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient Enumeration of At Most $k$-Out Polygons Akram, Waseem Yamanaka, Katsuhisa Computational Geometry Data Structures and Algorithms Let $S$ be a set of $n$ points in the Euclidean plane and general position i.e., no three points are collinear. An \emph{at most $k$-out polygon of $S$} is a simple polygon such that each vertex is a point in $S$ and there are at most $k$ points outside the polygon. In this paper, we consider the problem of enumerating all the at most $k$-out polygon of $S$. We propose a new enumeration algorithm for the at most $k$-out polygons of a point set. Our algorithm enumerates all the at most $k$-out polygons in $\mathcal{O}(n^2 \log{n})$ delay, while the running time of an existing algorithm is $\mathcal{O}(n^3 \log{n})$ delay. |
| title | Efficient Enumeration of At Most $k$-Out Polygons |
| topic | Computational Geometry Data Structures and Algorithms |
| url | https://arxiv.org/abs/2509.12696 |