Minimum-Weight Half-Plane Hitting Set
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911015549009920 |
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| author | Liu, Gang Wang, Haitao |
| author_facet | Liu, Gang Wang, Haitao |
| contents | Given a set $P$ of $n$ weighted points and a set $H$ of $n$ half-planes in the plane, the hitting set problem is to compute a subset $P'$ of points from $P$ such that each half-plane contains at least one point from $P'$ and the total weight of the points in $P'$ is minimized. The previous best algorithm solves the problem in $O(n^{7/2}\log^2 n)$ time. In this paper, we present a new algorithm with runtime $O(n^{5/2}\log^2 n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16979 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimum-Weight Half-Plane Hitting Set Liu, Gang Wang, Haitao Computational Geometry Data Structures and Algorithms Given a set $P$ of $n$ weighted points and a set $H$ of $n$ half-planes in the plane, the hitting set problem is to compute a subset $P'$ of points from $P$ such that each half-plane contains at least one point from $P'$ and the total weight of the points in $P'$ is minimized. The previous best algorithm solves the problem in $O(n^{7/2}\log^2 n)$ time. In this paper, we present a new algorithm with runtime $O(n^{5/2}\log^2 n)$. |
| title | Minimum-Weight Half-Plane Hitting Set |
| topic | Computational Geometry Data Structures and Algorithms |
| url | https://arxiv.org/abs/2506.16979 |