A set $\mathcal{D}$ of disks in the plane is said to be pierced by a point set P if each disk in $\mathcal{D}$ contains a point of P. Any set of pairwise intersecting unit disks can be pierced by 3 points (Hadwiger and Debrunner (1955) [7]). Stachó and independently Danzer established that any set of pairwise intersecting arbitrary disks can be pierced by 4 points (Stachó (1981–1984) [16]. Danzer (1986) [4]). Existing linear-time algorithms for finding a set of 4 or 5 points that pierce pairwise intersecting disks of arbitrary radius use the LP-type problem as a subroutine. We present simple linear-time algorithms for finding 3 points for piercing pairwise intersecting unit disks, and 5 points for piercing pairwise intersecting disks of arbitrary radius. Our algorithms use simple geometric transformations and avoid heavy machinery. We also show that 3 points are sometimes necessary for piercing pairwise intersecting unit disks.

一套$\mathcal{丁}$如果平面中的每个圆盘都被点集P刺穿$\mathcal{丁}$包含点P。任何一组成对相交的单位圆盘都可以被 3 个点刺穿（Hadwiger 和 Debrunner (1955) [7]）。Stachó 和 Danzer 独立地确定了任何一组成对相交的任意圆盘都可以被 4 个点刺穿 (Stachó (1981–1984) [16] . Danzer (1986) [4]). 用于寻找一组 4 或 5 个点的现有线性时间算法使用 LP 类型问题作为子程序。我们提出了简单的线性时间算法，用于找到 3 个点以刺穿成对相交的单位圆盘，并找到 5 个点以刺穿任意半径的成对相交圆盘。我们的算法使用简单的几何变换并避免使用重型机械。我们还表明，有时需要 3 个点来刺穿成对相交的单位圆盘。