A common sensing problem is to use a set of stationary tracking locations to monitor a collection of moving devices: Given $n$ objects that need to be tracked, each following its own trajectory, and $m$ stationary traffic control stations, each with a sensing region of adjustable range; how should we adjust the individual sensor ranges in order to optimize energy consumption? We provide both negative theoretical and positive practical results for this important and natural challenge. On the theoretical side, we show that even if all objects move at constant speed along straight lines, no polynomial-time algorithm can guarantee optimal coverage for a given starting solution. On the practical side, we present an algorithm based on geometric insights that is able to find optimal solutions for the $\min \max$ variant of the problem, which aims at minimizing peak power consumption. Runtimes for instances with 500 moving objects and 25 stations are in the order of seconds for scenarios that take minutes to play out in the real world, demonstrating real-time capability of our methods.

翻译：一个常见的感知问题是利用一组固定追踪位置来监控多个移动设备：给定 $n$ 个需要追踪的目标（每个目标沿各自轨迹运动）和 $m$ 个固定交通管制站（每个站点具有可调范围的感知区域），应如何调整各传感器的探测范围以优化能耗？针对这一重要且自然的挑战，我们同时提供了理论上的否定性结论与实践中的肯定性成果。在理论层面，我们证明即使所有目标均以恒定速度沿直线运动，也不存在多项式时间算法能保证对给定初始解实现最优覆盖。在实践层面，我们提出一种基于几何洞察的算法，能够求解该问题的 $\min \max$ 变体（旨在最小化峰值功耗）的最优解。对于包含500个移动目标和25个站点的实例，其运行时间仅为秒级，而实际场景的演化需要数分钟，这证明了我们方法具备实时处理能力。