两平行轴正方形最优覆盖和命中线段集的线性时间算法
A linear time algorithm to cover and hit a set of line segments optimally by two axis-parallel squares
摘要：
本文讨论了在${\mathbb R}^2$中用一对轴平行的正方形覆盖并击中一组线段$\cal L$，使得两个正方形中较大的一个的边长最小的问题.我们还讨论了限制版本的覆盖，其中每个线段在$\cal L$是完全覆盖的至少一个广场。所提出的算法的覆盖问题报告的最佳结果，通过执行只有两个通过读取的输入数据顺序。该算法在$O(n)$时间内得到最优解。所有提出的算法都是就地的，并且它们只使用$O(1)$额外的空间。这些问题的解也给出了用两个最小半径的全等圆盘覆盖和命中这些线段$\cal L$的$\sqrt{2}$近似，并且具有相同的计算复杂性.
英文摘要：
This paper discusses the problem of covering and hitting a set of line segments $\cal L$ in ${\mathbb R}^2$ by a pair of axis-parallel squares such that the side length of the larger of the two squares is minimized. We also discuss the restricted version of covering, where each line segment in $\cal L$ is to be covered completely by at least one square. The proposed algorithm for the covering problem reports the optimum result by executing only two passes of reading the input data sequentially. The algorithm proposed for the hitting and restricted covering problems produces optimum result in $O(n)$ time. All the proposed algorithms are in-place, and they use only $O(1)$ extra space. The solution of these problems also give a $\sqrt{2}$ approximation for covering and hitting those line segments $\cal L$ by two congruent disks of minimum radius with same computational complexity.
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