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arXiv · 2506.16979

Minimum-Weight Half-Plane Hitting Set

Gang Liu·Haitao Wang
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Abstract

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 $O(n^{5/2}\log^2 n)$.

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Gang Liu, Haitao Wang. 2025-06-20. Minimum-Weight Half-Plane Hitting Set. https://arxiv.org/abs/2506.16979

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