An Optimal Algorithm for Half-plane Hitting Set
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_ | 1866916550912507904 |
|---|---|
| author | Liu, Gang Wang, Haitao |
| author_facet | Liu, Gang Wang, Haitao |
| contents | Given a set $ P $ of $n$ points and a set $ H $ of $n$ half-planes in the plane, we consider the problem of computing a smallest subset of points such that each half-plane contains at least one point of the subset. The previously best algorithm solves the problem in $O(n^3 \log n)$ time. It is also known that $Ω(n \log n)$ is a lower bound for the problem under the algebraic decision tree model. In this paper, we present an $O(n \log n)$ time algorithm, which matches the lower bound and thus is optimal. Another virtue of the algorithm is that it is relatively simple. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02195 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Optimal Algorithm for Half-plane Hitting Set Liu, Gang Wang, Haitao Computational Geometry Data Structures and Algorithms Given a set $ P $ of $n$ points and a set $ H $ of $n$ half-planes in the plane, we consider the problem of computing a smallest subset of points such that each half-plane contains at least one point of the subset. The previously best algorithm solves the problem in $O(n^3 \log n)$ time. It is also known that $Ω(n \log n)$ is a lower bound for the problem under the algebraic decision tree model. In this paper, we present an $O(n \log n)$ time algorithm, which matches the lower bound and thus is optimal. Another virtue of the algorithm is that it is relatively simple. |
| title | An Optimal Algorithm for Half-plane Hitting Set |
| topic | Computational Geometry Data Structures and Algorithms |
| url | https://arxiv.org/abs/2501.02195 |