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- W4376988591 abstract "Given a set $P$ of $n$ weighted points and a set $S$ of $m$ disks in the plane, the hitting set problem is to compute a subset $P'$ of points of $P$ such that each disk contains at least one point of $P'$ and the total weight of all points of $P'$ is minimized. The problem is known to be NP-hard. In this paper, we consider a line-constrained version of the problem in which all disks are centered on a line $ell$. We present an $O((m+n)log(m+n)+kappa log m)$ time algorithm for the problem, where $kappa$ is the number of pairs of disks that intersect. For the unit-disk case where all disks have the same radius, the running time can be reduced to $O((n + m)log(m + n))$. In addition, we solve the problem in $O((m + n)log(m + n))$ time in the $L_{infty}$ and $L_1$ metrics, in which a disk is a square and a diamond, respectively. Our techniques can also be used to solve other geometric hitting set problems. For example, given in the plane a set $P$ of $n$ weighted points and a set $S$ of $n$ half-planes, we solve in $O(n^4log n)$ time the problem of finding a minimum weight hitting set of $P$ for $S$. This improves the previous best algorithm of $O(n^6)$ time by nearly a quadratic factor." @default.
- W4376988591 created "2023-05-18" @default.
- W4376988591 creator A5058637832 @default.
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- W4376988591 date "2023-05-15" @default.
- W4376988591 modified "2023-09-29" @default.
- W4376988591 title "Geometric Hitting Set for Line-Constrained Disks and Related Problems" @default.
- W4376988591 doi "https://doi.org/10.48550/arxiv.2305.09045" @default.
- W4376988591 hasPublicationYear "2023" @default.
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