街道网络的巡逻是强NP-完全的但对于树结构是P的
Patrolling a Street Network is Strongly NP-Complete but in P for Tree Structures
摘要：
我们考虑以下问题：给定平面上的一组有限的直线段，确定这些段上最少数量的点的位置，警卫可以从中看到所有段。这个问题可以被解释为寻找一个最小数量的位置的警察，警卫，摄像头或其他传感器，可以观察到网络的街道，走廊，隧道，管道等，我们表明，这个问题是强烈的NP-完全的，即使是一组段的三次图结构，但在P为树结构。
英文摘要：
We consider the following problem: Given a finite set of straight line segments in the plane, determine the positions of a minimal number of points on the segments, from which guards can see all segments. This problem can be interpreted as looking for a minimal number of locations of policemen, guards, cameras or other sensors, that can observe a network of streets, corridors, tunnels, tubes, etc. We show that the problem is strongly NP-complete even for a set of segments with a cubic graph structure, but in P for tree structures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
