方形作物地块的最小生成树
Minimum Spanning Trees for Square Crop Plots
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中文总结 AI 辅助
针对作物地块仅能通过特定入口/出口对访问的问题，研究单位正方形集合的最小生成树，证明其计算为 NP 困难，并给出因子 4 的近似算法。
中文摘要 AI 辅助
受田间作物地块可达性的启发，其中每个作物地块只能通过给定的入口/出口点对访问（我们有三种不同类型，每种包含四种情况），我们研究了此类轴对齐单位正方形平面集合对应的最小生成树（MST）问题。结果表明，尽管整个问题的设置是几何的，这种作物地块距离并不满足三角不等式。因此需要格外小心。本文的主要结果如下：（1）我们证明了在作物地块距离下计算单位正方形集合 $P$ 的最小生成树是 NP 困难的，（2）$P$ 的最小生成树可以用因子 4 的近似算法逼近。
英文摘要
Motivated by accessing crop plots in a field, where each crop plot can only be visited by a given pair of entry/exit points (we have three different types, each having four cases), we study the corresponding Minimum Spanning Tree (MST) problem of such a planar set of axis-aligned unit squares. It turns out that this crop plot distance does not satisfy triangle inequality, even though the whole setup of the problem is geometric. Hence additional care must be taken. The main results of this paper are as follows: (1) we prove that computing the MST of a set $P$ of unit squares under the crop plot distance is NP-hard, (2) the MST of $P$ can be approximated with a factor-4 approximation.
发表机构
- Gianforte School of Computing, Montana State University（蒙大拿州立大学吉安福特计算机学院）
机构由 AI 辅助整理，请以论文原文为准。
