闭合环上的连通性维护与屏障覆盖算法
Algorithms for Connectivity Maintenance and Barrier Coverage on a Closed Cycle
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中文总结 AI 辅助
本文针对闭合环上无线网络连通性维护问题，提出线性时间最优算法，改进后在不增加时间复杂度的情况下得到字典序最优解，可应用于移动无线网络及屏障覆盖场景。
中文摘要 AI 辅助
本文研究闭合环上无线网络的连通性维护问题。初始输入为n个位于闭合环上的点，这些点可沿环移动，若两点距离不超过给定值r则称二者连通。问题目标是移动这些点，使任意相邻点对直接连通——即沿环的两个相反方向都存在两点间路径——同时最小化所有点的最大移动距离。该问题源于移动无线网络的应用，包括在闭合轨道运行的传感器、车辆及卫星，也适用于屏障或边界覆盖问题，此类场景中传感器沿闭合边界部署，通过沿环重新定位实现覆盖。本文针对该问题提出了线性时间的最优算法，随后对算法进行改进，在不增加时间复杂度的前提下得到了字典序最优解。
英文摘要
The problem of maintaining connectivity of a wireless network on a closed cycle is studied in this paper. In the initial input, we have $n$ points located on a closed cycle. The points can move along the cycle, and if the distance between two points is at most a given value $r$, we say these two points are connected. The goal of the problem is to move the points along the cycle such that any adjacent pair of points is directly connected--i.e., there exist two paths between them in opposite directions along the cycle--while minimizing the maximum movement over all points. This problem is motivated by applications in mobile wireless networks, including sensors, vehicles, and satellites operating on closed orbits. It is also applicable to barrier or border coverage problems, where sensors are deployed along a closed boundary and coverage is achieved through repositioning along the cycle. We present a linear time optimal algorithm for this problem. Then we refine the algorithm to obtain a lexicographically optimal solution without increasing the time complexity.
