矩形障碍物的弱覆盖
Weak Coverage of a Rectangular Barrier
摘要：
假设n个无线移动传感器最初以自组织方式分散在矩形区域中。它们需要移动到最终位置，以便它们可以检测到任何沿平行于矩形边的方向穿过该区域的入侵者，从而提供该区域的弱屏障覆盖。我们研究了三个优化问题的传感器的移动，以实现弱屏障覆盖：最小化移动的传感器的数量（Minimums），最小化移动的传感器的平均距离（MinSum），最小化移动的传感器的最大距离（MinMax）。我们给出了一个O（n^{3/2}）时间算法的Minnesota问题的直径1的传感器，最初放置在整数位置;相反，我们表明，即使是传感器的直径2，最初放置在整数位置的问题是NP-困难的。我们表明，最小和问题是可解的在O（n log n）时间均匀的范围传感器在任意初始位置，而它是NP-hard的异质传感器范围。最后，我们证明，即使是非常有限的齐次版本的MinMax问题是NP-困难的。
英文摘要：
Assume n wireless mobile sensors are initially dispersed in an ad hoc manner in a rectangular region. They are required to move to final locations so that they can detect any intruder crossing the region in a direction parallel to the sides of the rectangle, and thus provide weak barrier coverage of the region. We study three optimization problems related to the movement of sensors to achieve weak barrier coverage: minimizing the number of sensors moved (MinNum), minimizing the average distance moved by the sensors (MinSum), and minimizing the maximum distance moved by the sensors (MinMax). We give an O(n^{3/2}) time algorithm for the MinNum problem for sensors of diameter 1 that are initially placed at integer positions; in contrast we show that the problem is NP-hard even for sensors of diameter 2 that are initially placed at integer positions. We show that the MinSum problem is solvable in O(n log n) time for homogeneous range sensors in arbitrary initial positions, while it is NP-hard for heterogeneous sensor ranges. Finally, we prove that even very restricted homogeneous versions of the MinMax problem are NP-hard.
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